Clear chances were few and far between at both ends of the field in what was the second London derby between the two teams in the space of a week.
Chelsea had the best openings, but Arsenal managed to grind out a second consecutive 0-0 stalemate at Stamford Bridge to leave them with the very slight advantage heading into the second leg at the Emirates Stadium in a fortnight's time.
Alexis Sanchez was left on the bench amid relentless speculation over his future, though, and Arsenal could have perhaps done with the Chilean on the field during a subdued start to the match.
Whereas the 2-2 Premier League draw between the two sides a week ago was action-packed from the first whistle to the last, it took until midway through the first half for either side to have a notable sight of goal this evening, and even then it was wasted by Alexandre Lacazette as he sliced an effort high and wide of the target after beating the offside trap.
Chelsea responded with their own chance two minutes later when Victor Moses cut inside before drilling a low strike towards the near post which David Ospina needed two attempts to collect with Cesc Fabregas lurking.
Moses came close again shortly before the half-hour mark with another left-footed snapshot towards the bottom corner, but once again Ospina was down smartly to deny the Chelsea wing-back, with a little help from the woodwork.
N'Golo Kante was the next to threaten with a wayward drive which flew over the crossbar before Arsenal registered their one and only shot on target of the first half as Alex Iwobi's strike from the edge of the box was parried away by Thibaut Courtois.
The best chance of a largely uneventful first half came right on the stroke of half time, though, as Fabregas latched on to Cesar Azpilicueta's trademark cross from deep only to plant his header straight at Ospina.
The second half got off to a brighter start for Chelsea as they put their London rivals under some early pressure after the restart, with Andreas Christensen the first to threaten when he failed to steer a header on target after Marcos Alonso had flicked the ball on to him at the back post.
Alonso almost opened the scoring himself shortly afterwards when he was a whisker away from glancing Fabregas's corner home, and Morata could not bring the ball under his spell when it fell to him inside the six-yard box either.
Morata spurned a host of chances in the recent Premier League meeting between the two sides, but he was enjoying a growing influence on the game and came close to opening the scoring twice in quick succession shortly before the hour mark.
The first saw the Spaniard turn into space before quickly releasing a 25-yard effort which Ospina needed to parry away, before Morata then rolled Shkodran Mustafi to race through on goal and squeeze his finish under the onrushing Arsenal keeper, only to see it trickle into the side-netting.
It was Chelsea who continued to look the most like scoring, though, and Moses saw a vicious low drive deflected over from Mustafi before Ospina was left in no-man's land from the resulting corner, only for Christensen to plant his header wide of the target with the goal gaping.
There were more routine saves for both Ospina and Courtois towards the closing stages, and Fabregas also saw a deflected cross strike the outside of the post with two minutes of normal time remaining, but by the end of the match it felt as though both teams could have played on for a while without breaking the deadlock - a far cry from their meeting just seven days ago.
The result means that all three competitive fixtures between the two sides this season have ended in draws, with one more to come when Arsenal welcome Chelsea to the Emirates for the return leg later this month.
Chelsea have now drawn three games in row for the first time since January 2013 and have failed to win their opening three games of a calendar year for the first time in 25 years, while it is only the second time in Arsene Wenger's tenure that Arsenal have also been left winless three games into a new year.
Chelsea will now turn their attention to the Premier League visit of Leicester City on Saturday, while Arsenal face a trip to Bournemouth on Sunday as they look to end a four-match winless streak across all competitions.
CHELSEA (3-5-1-1): Courtois; Azpilicueta, Christensen, Rudiger; Moses, Drinkwater (Willian, 68'), Kante, Fabregas, Alonso; Hazard (Bakayoko, 84'); Morata (87')
ARSENAL (3-4-3): Ospina; Chambers, Mustafi, Holding; Bellerin, Xhaka, Wilshere (Elneny, 57'), Maitland-Niles; Iwobi, Lacazette (Sanchez, 66'), Welbeck