The tie helped RSL (9-9-7) salvage a point in the Western Conference standings and prevented a potentially damaging loss.
It also gave RSL a 7-1-5 home field record.
Both clubs had late winning chances, but goalies Nick Romando of RSL and Jon Busch of Chicago made critical saves in the closing minutes.
The Fire (10-6-9) got a goal from Chris Rolfe, his sixth this season, in the 44th minute, while Busch made a sliding save on an early shot by RSL's Pablo Campos.
Senate Democrats to pull all-nighter on climate change
Susan Sarandon 'very excited' about daughter's pregnancy