The suspect has been taken into custody and an investigation is underway, Efe news agency reported.
The incident began when a shooting occurred at 1.30 p.m. in Newton Division after which the suspect fled the scene, the Los Angeles Police Department said on Twitter.
Police located the suspect and a pursuit ensued "at which point the suspect fired multiple rounds at pursuing officers," it added.
"The suspect then crashed his vehicle at which point an officer involved shooting occurred. At the termination of the pursuit, the suspect fled into the Trader Joe's," police said.
"Inside the Trader Joe's, a female victim was struck by gunfire. She was pronounced dead at scene," it added.
The suspect held multiple people hostage in the store before the suspect walked out and "asked that he put handcuffs on himself," police said.
He was then taken into custody.
It was not clear how many people were inside the store in Silver Lake neighbourhood and whether there were any other casualties.
Los Angeles Mayor Eric Garcetti had earlier said on social media that 100 firefighters and 18 ambulances had been deployed as well as the Mayor's Crisis Response Team "to provide emotional support and resources to victims of #Silverlake #TraderJoes incident."
US President Donald Trump said on Twitter he was "watching Los Angeles possible hostage situation very closely. Active barricaded suspect. L.A.P.D. working with Federal Law Enforcement."
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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