RSL (0-3-5) played on the road for the third time in eight days and came to Bridgeview without a win, while Chicago (3-4-2) had dropped its previous four games.
In the seventh minute, Freddy Adu tried to put RSL ahead, but his floater was stopped by Fire goalkeeper Matt Pickens, who made seven saves.
Chicago forward Chad Barrett had a one-on-one in the 14th minute and was able to break free from an RSL defender, but his shot was halted by RSL keeper Nick Rimando, who dove to his right for seventh save as well.
Next up for RSL is a trip to New England June 2, while the Fire is home against Columbus June 3.
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