The man fired a single gunshot, killing himself just as police tried to serve him with a search warrant at Harvey Apartments on Santa Monica Boulevard, reports CBS News National Correspondent Ben Tracy. Police called him "a person of interest" in the investigation.
Tracy says the suicide may prove to be a break in Chasen's brutal murder. Detectives armed with questions and a search warrant entered the lobby of the Harvey Apartments on what they thought was a follow-up call.
But the man backed away and refused orders to raise his hands.
Capt. Kevin McClure of the Los Angeles Police Department tells CBS News that when his officers tried to talk to the man, "the suspect produced a hand gun and there was a self-inflicted gunshot wound at that point in time."
Police have not released the man's name or revealed any possible connections to the Beverly Hills publicist, but they have apparently been tracking his movements.
Andrew Blankstein, a crime reporter for the Los Angeles Times, says Beverly Hills police had been watching people come and go from the apartment building for days, "or perhaps longer."
One neighbor told the Los Angeles that the man he knew only as "Harold" told him he was an ex-convict who twice served time in state prison. He also claimed he would be receiving $10,000, but gave different reasons for coming into the money.
Many remain stunned by Chasen's violent death. She was shot five times in the chest at a Beverly Hills intersection on November 16. No shell casings were found at the scene, but her killer fired a nine-millimeter handgun loaded with at least one hollow point bullet, according to a partial coroner's report.
Those details, says Tracy, may point to a targeted hit -- possibly involving the suicide victim.
"What role did he play? Did he act alone? Did he act on behalf of others," ponders Blankstein. "These are the big questions police are going to have to answer as this investigation goes forward."
Speaking Thursday on "The Early Show," Criminal profiler Pat Brown speculated that the man who shot himself "knew he was going down for something big."
"He knew he was going back to prison for the rest of his life. As a matter of fact he told somebody, 'I'd kill myself before I let that happen.' He clearly knew he would be arrested for something more than petty larceny. I would say, yes, he's connected."
A retired Los Angeles Police investigator suggested the tight grouping of bullet wounds in Chasen's chest indicated the killer was a "professional," but Brown took issue with that assessment.
"He said that because of the type of ammunition, which was hollow-points -- nine-millimeter with hollow points -- but I hate to tell him, I've got the same thing in my house in my gun, I have a nine-millimeter with hollow points. If I was that close -- this person either stood next to the car and shot into it or drove up to the car and fired into it almost point-blank range, I could shoot that pattern," said Brown. "I don't think he is a professional, but he could be a hired thug. If he killed himself, this guy is a felon, he knows his weapons, and may have been paid to do it, but I wouldn't call him a professional, just a guy hired to kill somebody."
Brown says it's likely the entire story of Chasen's death will eventually come out.
"There has to be some reason (the police) rolled in on this guy. There were no witnesses, as far as I know. He could have been stupid enough to lean on the car when he shot with his hand, you know, some people did dumb things like that. But there may have been a connection, some connection by cell phone or some kind of message that they got that sent them to that particular location, which is why they were watching it," she speculated.
"What's interesting to me is the fact she was shot in the chest," noted Brown.
"Usually close up, you go for the head. So either he just had the angle to shoot for the chest or somebody said don't shoot her in the face and that might be an emotional connection, so might be looking for somebody close to the woman, maybe, who had a lot of problems, gambling debts or something, maybe somebody in the will. I think they have a connection close to Ronni Chasen," suggested the criminal profiler.