Kaepernick, who replaced the injured Alex Smith, was outstanding his his first career start, prompting Harbaugh to say that the Niners would "go with the hot hand" next Sunday against the New Orleans Saints.
"I usually tend to go with the guy that has the hot hand and we have two quarterbacks that have a hot hand," Harbaugh said after Monday's 32-7 victory. "So I thought Colin did an outstanding job. I thought he did a great job, poised in the pocket pushing the ball throwing with accuracy, did a nice job running the game plan. Everything he did was exemplary and really acquitted himself great, very proud of him for that."
Kaepernick, who had played sparingly since being drafted in the second round last year, completed 16 of 23 passes for 243 yards and two touchdowns against Chicago's vaunted defense.
"It's everything I could've ever wished for," Kaepernick said. "It feels great just to be out there."
Harbaugh acknowledged he was "impressed" with Kaepernick and dismissed the notion that Smith shouldn't lose his starting job because of an injury.
"We'll make that determination as we go, but there's no rule," Harbaugh said.
Smith, who had made 28 consecutive starts, suffered a concussion in last week's tie against the St. Louis Rams and was ruled out against the Bears after failing to receive clearance from a neurologist.
Harbaugh said that he had already decided to start Kaepernick when Smith, who is ranked third in the NFL with a 104.1 passer rating, still was experiencing headache symptoms as recently as this past Sunday.
Kaepernick was quick to reward Harbaugh for his decision, throwing for 184 yards in the first half alone.
"I think after the first drive I felt really comfortable with what they were doing and what we had in our game plan," Kaepernick said. "I really wasn't too nervous. I've had a lot of time in this offense. My teammates were really supportive."
Information from The Associated Press was used in this report.