The Chicago Tribune reports that the shooter was eventually apprehended and was wearing a protective vest.
The suspect is a four-time convicted felon named Shomari Legghette, according to WGN News.
Chicago Mayor Rahm Emanuel was visibly emotional while discussing Bauer's wife, Erin, and daughter, Grace, saying, "Erin and Grace, we love you, the Bauer family, the family of CPD, 2.8 million Chicagoans, we are holding you in our hearts". He's the first Chicago officer to be killed in seven-years, and the highest ranking officer to be killed in decades.
Bauer was rushed to Northwestern Memorial Hospital, where he was pronounced dead a short time later.
"Some people don't deserve to walk the streets of Chicago", Chicago police superintendent Eddie Johnson said.
Paul Bauer gave up his life in service to the city, and his brothers and sisters in blue were paying tribute to their longtime friend Wednesday morning, a day after he was gunned down by an assailant in the Loop.More news: Snow in the forecast for MA this weekend
A procession of law enforcement vehicles took Bauer's body to the medical examiner's office. Officers had been chasing the man on foot.
Before working with the 18 District, Bauer served in the Chicago Police Mounted Patrol Unit.
Police said surveillance video captured a struggle between the two inside the stairwell with the suspect pulling Bauer down the stairs. "We're not talking about the guy who stole a loaf of bread from the store to feed his family", he said in November 2017. We're talking about career robbers, burglars, drug dealers.
Witnesses to parts of the incident near said they heard gunshots. He arrived in Chicago around 7 p.m. and headed straight to a meeting with Johnson, the mayor's staff said. "They need to be off the street".
"I could count on Paul to come and help me with this right now", he said.
"There was no communication from him on the radio informing dispatch that he was in pursuit of the offender or that he was even on scene, so they initially thought it was an off-duty officer until someone recognized him", spokesman Anthony Guglielmi wrote in an email.
Chicago's continuing battle with criminal violence is illustrated by the fact he was not the only shooting victim in the long-suffering city on Tuesday.