Adam Buksa scored in the 14th minute for the Revolution, who were thwarted in their bid to record their first opening day win since a 1-0 victory over Chicago to begin the 2013 season. New England goalkeeper Matt Turner overcame a rocky start to finish with five saves.
New England's Edward Kizza nearly netted the go-ahead goal in the 87th minute, however his header caromed off the crossbar.
Robert Beric collected a goal and an assist and Luka Stojanovic also tallied for the Fire, who were denied in their bid to secure their first opening-day victory since posting a 3-1 win over FC Dallas in 2009. Bobby Shuttlesworth finished with three saves for Chicago.
Beric, who erupted for a team-high 12 goals last season, wasted little time setting the tone for the contest. Boris Sekulic's deft centering feed allowed Beric to convert into an open net in the fifth minute.
Chicago kept the pressure on and doubled the advantage in the 11th minute. Przemyslaw Frankowski's cross found Beric, who set up an unmarked Stojanovic for the latter's first MLS goal.
Buksa, who scored a goal in a 1-1 draw against the Fire on March 7, 2020, halved the deficit in the 14th minute off a set piece. Captain Carles Gil's service off a corner kick found Buksa, who sent a header inside the right post.
The Revolution forged a tie in the 27th minute, with Bou tapping home a service from Tajon Buchanan.
Buksa nearly gave New England the lead during first-half stoppage time, however his header off a cross from Gil sailed just wide of the net.