Lionel Messi's wonderful free-kick had given Argentina a lead in the game Eduardo Vargas (57) scored an equaliser in the second half to ensure his side was still in the game.
Argentina dominated Chile in the first half but still managed to net only one goal before the essay concluded.
Vargas levelled the scoreboard after the break as Chile took a sigh of relief. The final 30 minutes saw Argentina again dominating the game however this time the side wasn't able to break Chile's defence.
Argentina are now eleven games unbeaten against Chile in all competitions. Argentina will next face Uruguay while Chile takes on Bolivia on Friday.
Earlier, Paraguay thrashed Bolivia 3-1. Erwin Saavedra had given Bolivia the lead from the penalty spot but a goal from Alejandro Romero Gamarra and two from Angel Romero helped Paraguay register the win.
Rio de Janeiro [Brazil], June 15
Argentina and Chile shared the points as the teams played out 1-1 draw in Rio de Janeiro in the ongoing Copa America.
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