Chasen was shot in Beverly Hills while driving home from a star-studded Hollywood film premiere, in a mystery that shocked the well-heeled celebrity neighborhood.
Police had revealed no leads or motives until Wednesday's incident, in which the suspect -- described as a tall, thin black man in his 40s, called Harold -- shot himself shortly after 6:00 pm in an apartment on Santa Monica Boulevard.
Beverly Hills police only said they were "conducting a follow-up investigation" at the apartment block, but the LA Times quoted sources saying he was a suspect in Chasen's death, and shot himself when confronted by police.
According to the newspaper, the police -- who had had the man under surveillance for some time -- were told he would be at the apartment on Wednesday evening.
When officers approached him in the lobby of the building, he backed up and refused their orders to put his hands up. The man then pulled out a pistol and shot himself in the head, sources told the LA Times.
Resident Brandon Harrison told the Times that the man described himself as an ex-convict, who had been jailed twice and did not want to go back behind bars.
"He told me several times, 'If it ever came back down to me going to prison, I would die first'," he said, adding that the man moved in to the apartment some months ago, but had been evicted.
"The man was very strange," he told the newspaper.
A former neighbor, Terri Gilpin, said the man recently bragged that he had killed Chasen and was going to get paid for it.
"He bragged all the time that he was the one who killed the publicist, and he was always talking about how he was going to get paid 10,000 dollars for it," Gilpin told a local TV station.
A resident of the apartment block, who gave his name only as Pete, said the suspect always had his bicycle with him, and talked about it with neighbors when he met them.
Chasen was shot five times in the chest shortly after midnight on November 16, hours after attending a glittering film premiere of "Burlesque" starring Christina Aguilera and Cher.
The 64-year-old, who publicized films like "Driving Miss Daisy" and "Robin Hood: Prince of Thieves," went on to an after-party and was driving home in her Mercedes when she was killed.
Officers found her car crashed into a light pole just off Sunset Boulevard.
In her will, a copy of which was published by TMZ on its website, Chasen left most of her assets to charity or to her niece Melissa Cohen.
Another niece, Jill Cohen, does not fare so well.
"I have intentionally and with full knowledge of the consequences omitted to provide for my niece, Jill Cohen, also known as Jill Gatsby, except for the gift of 10 dollars" Chasen wrote in the 1994 will.
A well-known figure in Hollywood film circles, Chasen previously served as vice president of publicity at MGM studios. Her death was the third homicide in Beverly Hills this year. The neighborhood had no homicides last year.