The upside: Even the worst defeats tend to feature a bright spot or two.
Cornerback Cortland Finnegan intercepted a pass, giving him one pick in each of the Rams' first three games.
Defensive end Chris Long collected two sacks. Long also had three quarterback hits and two tackles for loss.
Rookie kicker Greg Zuerlein made both field-goal tries, one from 56 yards and another from 46. He has made all eight attempts this season, five of them from at least 40 yards.
Steven Jackson was able to start the game after a groin injury had caused him to miss practice.
The Rams held Chicago to 3.0 yards per rushing attempt. That included one quarterback scramble covering 21 yards.
St. Louis held Jay Cutler without a touchdown pass while holding the Bears to 29 percent conversions on third down.
The Rams trailed only 13-6 with 10 minutes left in the third quarter.
Looking ahead: The Rams are home against the Seattle Seahawks in Week 4.