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“We have successfully taken the suspect into custody without incident,” the LAPD tweeted after a three-hour siege.
People were seen fleeing the Trader Joe’s supermarket, some jumping from windows. One woman was killed.
The suspect earlier fired shots as police pursued his car. He crashed the car and ran inside the shop. The chase began after he had shot two women.
The suspect, who is believed to a 28-year-old African-American, gave himself up after crisis negotiations with police in the Silverlake area, the LAPD said.
The suspect had asked that he put handcuffs on himself before leaving the shop, the LAPD said. He had an arm injury.
A young woman inside Trader Joe’s was shot and killed by the suspect, police said. She has not been identified.
“I regret to inform you that there is one fatality that occurred inside, of a woman,” Mayor Eric Garcetti said.
Earlier, terrified shoppers and staff were seen fleeing in panic - some jumping from windows, others climbing down a rope ladder.
Helicopter news footage showed two children being carried to safety by heavily armed police officers.
The suspect also released some people himself, the police said.
Eyewitness Don Kohles said he saw the car the suspect was driving crash into what was a fire hydrant or a utility pole.
“Then this guy comes out of the car and starts running toward TJs,” Mr Kohles told CNN.
“I look behind me and there were two police guys coming with heavy guns, then boom boom boom boom, so I go into TJ’s and I see this guy and he comes in.
“And I see the two front glass doors shot out. I look around and I see a TJ’s employee laying on the ground.
“We all laid there for about a half-an-hour until LAPD came and got us out. They helped carry me across the parking lot and they sort of tossed me over a wall,” Mr Kohles added.
During the stand-off, a woman was taken from the crashed car and transported to a local hospital.
She is believed to have been injured and forced into the vehicle after the gunman shot his grandmother and took her car.
The grandmother, shot a number of times, was in a critical condition, police said.
US President Donald Trump tweeted that he was watching the situation “very closely”. (UNI)