The hosts had the better openings of an anticlimactic contest just a week after they had played out a thriller in the league, with Cesc Fabregas and Andreas Christensen both squandering presentable headed chances.
The draw leaves Arsenal with the slightest advantage heading into their home second leg, which will take place at the Emirates Stadium in a fortnight's time.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute coverage below.
Thank you very much for joining Sports Mole for tonight's EFL Cup semi-final first leg as Chelsea and Arsenal play out another draw - this time a goalless one at Stamford Bridge. I will leave you with our match report and be sure to stick around for reaction from both camps too.
From me, though, it is goodbye for now!
Chelsea just about shaded the game in terms of chances and overall play, but they didn't do enough to win the game and neither keeper was really forced into any saves that they wouldn't have expected to make. The very slight advantage lies with Arsenal ahead of the second leg at the Emirates later this month!
Shots on target: 3-1
Aside from that the best opening for the Gunner fell to Lacazette midway through the half when he beat the offside trap to latch on to Wilshere's through-ball, only to line slice a poor finish high and wide of the target.
Ospina has been the busier of the two keepers so far, though, also being called into action to deny Victor Moses at his near post on a couple of occasions.
We are still goalless between Chelsea and Arsenal and clear chances have been few and far between, with only one you could describe as a really good opening.
CHELSEA STARTING XI: Courtois; Azpilicueta, Christensen, Rudiger; Moses, Kante, Fabregas, Drinkwater, Alonso; Hazard, Morata
ARSENAL STARTING XI: Ospina; Chambers, Mustafi, Holding; Bellerin, Wilshere, Xhaka, Maitland-Niles; Iwobi, Lacazette, Welbeck
Most will be hoping that there is no need for it tonight, but Arsenal have had a couple of contentious penalties given against them in recent weeks - including against Chelsea just seven days ago - so I'm sure Arsene Wenger will welcome the technology despite still being banned from the touchline for his comments regarding one of those penalties.
That is a major improvement on a record of only one win from their last 13 Premier League meetings - including draws in both this season - while Arsenal have won just one of their last nine visits to Stamford Bridge across all competitions, losing seven of those.
The most recent of those was a 2-0 win at the Emirates Stadium in the fourth round in October 2013 when Azpilicueta and Juan Mata got the goals, and the record also includes a semi-final victory en route to winning the trophy in 1997-98, with the Blues running out 4-3 winners on aggregate then.
Wenger hinted at the possibility of more caution from his side in the build-up to this match, but that is really not Arsenal's style and hopefully we will see another open and attacking game tonight, as it was a week ago. Chelsea have the stronger team out and the home advantage, though, so I will have to go for a home win.
SPORTS MOLE SAYS: Chelsea 2-0 Arsenal
Like Chelsea, all of Arsenal's EFL Cup games so far this season have come at home, and even then they have only managed to scrape past Doncaster, Norwich after extra time and West Ham, each by a one-goal margin.
If only away form counted in the Premier League this season the Gunners would be languishing down in ninth place, with just 13 points from their 11 away outings and only 13 goals too - compared to 26 points and 27 goals from the same number of home games.
Another defeat tonight would mark successive losses for the first time since August, and fans will not be particularly optimistic considering that they have also only won one of their last five - and two of their last eight - away games across all competitions.
No team has been knocked out in the semi-finals more often, though, with Arsenal losing seven of their previous 14 appearances in the last four and then going on to win just two of the seven finals they have reached.
Indeed, Arsenal have won the FA Cup a staggering eight times since they last lifted this trophy in 1992-93, with the Gunners having only reached the final of the competition twice under Wenger, losing in 2007 and 2011.
The 'Wenger Out' brigade have been comparatively quiet so far this season, but they are sure to be in full voice now and reports have even emerged suggesting that former Chelsea boss Carlo Ancelotti is being lined up as a replacement at the end of this season.
The Gunners became the first holders to be knocked out by lower league opposition since Swansea beat Portsmouth in 2009, conceded four goals against lower league opposition in the FA Cup for the first time since 1908, and were also eliminated in the third round of the competition for the first time in Arsene Wenger's tenure.
Stretching even further back, Chelsea have now lost only one of their last 16 games across all competitions - including 10 wins - although they have drawn their last two and another stalemate tonight would make it three on the bounce for the first time since January 2013.
Arsenal are the only team to have come away from Stamford Bridge with a draw in the Premier League this season, incidentally, although Conte's side have also fallen to two league defeats in front their own fans this term.
Across all competitions Conte's side are unbeaten in their last 11 home games, winning nine of those and drawing two. Indeed, the Blues have won nine of their last 10 and each of their last four, scoring 10 goals and keeping three clean sheets during the latter run.
There has been a slightly worrying trend in this season's competition in that Chelsea have conceded a goal in the 90th minute of each of their ties so far, although they have also scored twice in the final minutes en route to wins over Nottingham Forest, Everton and Bournemouth.
The only exception in that run came under Rafael Benitez against Swansea in 2012-13, but just two years later they were victorious in the last four and went on to lift the trophy at Wembley.
Even so, it is difficult to juggle four competitions, particularly considering they had no European football to worry about last season, so it will be interesting to see how they cope with that over the coming weeks.
This one is certainly their most likely to produce silverware having reached the semi-final stage, but it won't come easy with Arsenal and then most likely Man City standing in their way.
The match may not be quite as open an affair as the recent 2-2 draw in the Premier League given that there is still another leg to come after this one, but plenty were predicting a low-scoring encounter a week ago so hopefully these two produce another thrilling spectacle tonight.
Bellein, who scored the late equaliser between these two sides a week ago, is another big name to return to the side this evening, but behind him Ospina keeps his place ahead of Cech in goal. On the bench, meanwhile, is new signing Mavropanos, who could make his debut for the Gunners tonight.
Wenger was heavily criticised for his team selection at the weekend and he makes six changes from that team tonight, but there is only so much he can do with Ramsey, Giroud, Monreal, Koscielny and Kolasinac all currently sidelined through injury.
Wenger confirmed during his press conference that the midfielder will be fined if the stories turn out to be true, but that doesn't stop him naming Iwobi in his starting lineup for tonight's game in a front three alongside Lacazette and Welbeck.
In his pre-match press conference Wenger would not be drawn on whether Sanchez would be involved tonight, and if he does feature then it will have to be from the bench. Man City are understood to be closing in on a deal for the Chilean, so Arsenal fans will wonder whether every time they see him now will be the last they see of him in an Arsenal shirt.
Morata watched on from the bench as Chelsea failed to score with Batshuayi leading the line at the weekend, while Batshuayi also started against Bournemouth in the last round, but the Spaniard does get his chance in this competition tonight.
One more side note is that new signing Ross Barkley misses out as expected, with the former Everton man still working his way back up to match fitness.
The Belgian has terrorised Arsenal at times in the past and was on top form again a week ago, scoring his side's equalising goal from a penalty which he himself won, albeit in controversial circumstances. Conte is unlikely to ben risking Hazard if there were any lingering doubts over his fitness, so expect to see him at full throttle tonight.
Moses and Kante are also amongst the first-team players to come back into the side - both from the FA Cup and the last round of this competition - as Zappacosta and Bakayoko are amongst those to drop out.
We'll start with the home side, who have named a very strong starting lineup for tonight's game to leave us in no doubt that they are taking this competition seriously. Indeed, you could go as far as saying that it is the strongest team available to Antonio Conte at the moment.
There are changes galore from the last round - seven in total - and that starts right at the back with Thibaut Courtois, who put in a stunning performance when the two sides met a week ago despite conceding two goals, replacing Caballero in the side.
Manchester City took one step towards reaching Wembley with a late and narrow victory over Bristol City last night, and now it is time for the pick of the fixtures in the last four as London rivals Chelsea and Arsenal do battle for the second time in the space of a week. If we get even half as much action as last Wednesday's Premier League clash then we will be in for a good game tonight, and whatever happens it promises to be an intriguing contest between two teams who will see this competition as their most realistic chance of silverware this season.
We will have a closer look at both teams a little later, but first let's check out the team news...