Detectives said the victim was walking down the street with another woman when the suspect approached the two and they all began arguing before the suspect walked away on the 11700 block of Compton Avenue.
"The suspect then turned around and came up from behind the women and fired a handgun at the victim, striking her," said Los Angeles Sheriff's Deputy Benjamin Grubb. "The suspect then chased the other woman and fired at her but missed."
The victim was taken to a hospital and later pronounced dead. The victim's name has not been released.
The suspect fled on foot in an unknown direction.
City News Service contributed to this story