Both teams were taking to the field for the first time since the World Cup finals in Brazil and neither could find the back of the net at Levi's Stadium in Santa Clara.
Substitute Javier Orozco had a golden opportunity to make himself an instant hero in the 66th minute after only being on the pitch for a matter of seconds but the Santos Laguna striker skied his effort over the crossbar with an empty net at his mercy.
Chile are back in action against minnows Haiti in their final match in the USA on Tuesday, while Mexico face Bolivia on the same day.
Jorge Sampaoli only made one change to the Chile team that lost to Brazil in the last 16 at the World Cup, with Rodrigo Millar replacing Eduardo Vargas in the starting XI in the first of two games in the USA.
Arturo Vidal took his place in midfield after Sampaoli denied suggestions over the weekend that the Juventus star required surgery on his knee, while captain and goalkeeper Claudio Bravo joined Leonel Sanchez (1955-68) as Chile's most capped player with 84 appearances.
Miguel Angel Herrera and Oswaldo Alanis were handed debuts by Mexico coach Miguel Herrera, who also included Miguel Ponce and Jose Vazquez.
Captain Rafael Marquez, Hector Moreno, Miguel Layun and retired full-back Carlos Salcido made way for Mexico's first match since losing to the Netherlands in the round of 16 in Brazil.
Arsenal forward Alexis Sanchez had the first sight on goal after his effort from an acute angle flashed just wide of the post in the ninth minute.
Chile came close again to opening the scoring after 17 minutes, this time through sough-after midfielder Vidal, who had his header tipped over for a corner by Mexico goalkeeper Guillermo Ochoa.
Giovanni dos Santos almost put Mexico ahead in the 32nd minute, albeit fortuitously, when Chile failed to clear their lines, but the Villarreal striker failed to make contact with the ball inside the six-yard box.
Ochoa was forced into action early by Millar seven minutes in the second half after Sanchez played the ball in between two defenders for the Guadalajara man to shoot on goal.
Orozco wasted a great chance within seconds of replacing a hobbling Dos Santos in the 65th minute, fluffing his attempt on goal after finding himself unmarked six yards out.
