Both nations are looking to win the tournament for the first time in its history, having each come close to lifting the trophy in recent years.
The host nation made a winning start to the competition with a 2-0 victory over Ecuador in their opening match in Pool A, leaving them at the top of the table with the top two progressing to the knockout stage.
In that match, Juventus's Arturo Vidal converted from the penalty spot, giving Chile their first successful spot kick in the Copa since they last hosted the tournament in 1991.
Victory in this match would all but book Jorge Sampaoli's side's spot in the last eight, with all of the other sides in their group having dropped points in their opening matches, and group minnows Bolivia still to come in their final pool fixture.
The 19th best side in the world, according to FIFA's latest rankings, have been in mixed form coming into the tournament though, following up friendly defeats to Brazil and Iran in March with a narrow 1-0 victory over El Salvador earlier this month.
Chile have never won either the Copa or its predecessor, the South American Championship, but they were beaten finalists in 1987, and finished fourth in 1999.
In fact, Chile are the most successful side in the Americas never to have won the competition, finishing as runners-up on four occasions, including in 1955 when they were also the hosts.
Recent form: LWLLWW
Mexico have been the nearly-side in Copa American in recent editions of the competition, finishing third in three of the last six tournaments, while finishing as runners-up to Colombia in 2001.
The side currently ranked 22nd in the world will not have been happy with their start to the competition, being held to a goalless draw by Bolivia, the lowest-ranked side in South America, in their opening fixture.
However, victory over Chile in this match would definitely keep them in the top two heading into the final round of fixtures in the group stage, although they have a tricky tie against Ecuador still to come.
Miguel Herrera's side have won just one of their last five internationals, easing to a 3-0 win over Guatemala in a friendly back in May.
Their final two warm-up games for this tournament resulted in a draw with Peru and a defeat to Brazil, but they did record back-to-back victories over Ecuador and Paraguay in a tour of the USA earlier this year.
Recent form: WLWDLD
Chile will be without Matias Fernandez for the fixture after the midfielder was sent off late in the win over Ecuador.
With Gonzalo Jara also on a booking, Sampaoli may choose to rest the defender, ensuring that he will be available for the potentially-crucial final group stage match.
Eduardo Vargas may have done enough to earn a place in the starting lineup this time out, having come off the bench to score the second goal for Chile last time out.
Meanwhile, Mexico may look to make changes up front, having failed to find the back of the net in their opening fixture of the competition.
Like Chile, Mexico may also be wary of picking up bookings, with Gerardo Flores just one more yellow away from suspension from the clash with Ecuador.
Chile possible starting lineup:
Bravo, Mena, Medel, Rojas, Isla, Pizarro, Aranguiz, Diaz, Sanchez, Vidal, Vargas
Mexico possible starting lineup:
Corona, Dominguez, Ayala, Marquez, Flores, Aldrete, Corona, Montes, Jimenez, Montes, Fabian
Head To Head
It has been less than a year since these two sides last played, sharing a goalless draw in a friendly on neutral ground last September.
There has been little between the pair in recent years, with their last six meetings resulting in two wins for each side and two stalemates, with all the victories coming by an odd goal.
Their last competitive meeting was back in the 2011 Copa America, with Chile coming away with a 2-1 win, but Mexico have the advantage in their total of 12 meetings, winning six times, and losing just three matches.
We say: Chile 2-1 Mexico
Recent history suggests that this will be a closely-fought fixture, but Chile certainly looked the stronger of the two in the opening round of fixtures. The host nation should not need to make too many changes to their side, while Mexico still need to find their strongest XI. Chile will also have the added bonus of having the home crowd behind them.