The incident began when the still unidentified suspect, who is now in custody and receiving treatment for a gunshot wound to his arm at Los Angeles County Medical Center, allegedly shot his grandmother and girlfriend in a domestic dispute in the 1600 block of East 32nd Street, about 2 1/2 miles east of USC.
Details on how the woman died inside the store were not immediately known.
Los Angeles Police Department tweeted: "There is an active police incident at the Trader Joe's near the intersection of Hyperion Ave and Griffith Park Blvd in Silverlake".
Officers were able to track the auto using LoJack - a stolen vehicle tracking system - and officers tried to stop the auto in Hollywood, but the man refused to pull over, Moore said.
Police amassed outside the store, and at 5:30 p.m., at least three people who appeared to be customers came out of the store with their hands in the air - apparently hostages who were released or shoppers who had managed to elude the gunman.
Police officers escort people out after sealing off the area near Trader Joe's supermarket.
He asked that he put handcuffs on himself before leaving the shop. He then fled in a auto with officers pursuing him through the city.
Around 1:30 p.m., police spotted the suspect driving his grandmother's vehicle in the Hollywood area and a pursuit began. Lopez says the suspect shot multiple rounds at officers during the chase but no officers were struck.
People were earlier seen running from the Trader Joe's supermarket. Police officers gave chase through Hollywood, ending with the man crashing his vehicle outside the Trader Joe's, and barricading himself inside the store.
There was one fatality, police said.
About 40 people were inside the grocery store on Hyperion Avenue in the Silver Lake neighborhood when an armed man ran in, according to police.
The suspect had a pistol in his hand and "just started opening fire on the police behind him", Field said.
People frantically tried to flee from the store and some were seen climbing through windows, jumping down and others darted through the back door. He crashed the vehicle attempting to escape police, firing at officers before running into the nearby grocery store.
CNN spoke to employees at nearby Jersey Mikes and What the Fish, both stores are on lockdown and no one was injured. SWAT teams also arrived on the scene as the news of the incident gathered steam in the media. She was a store manager.
He then saw five employees hang out a second-floor window and drop to the ground and around 15 others run to safety from the back of the store.
LAPD Asst. Chief Robert Arcos said in a press briefing that a shooter is "barricaded" in the store.
Employees and customers inside the store dove for cover as the bullets flew.
A suspect wanted in connection with a shooting was barricaded inside a supermarket in the U.S. city of Los Angeles on Saturday, police said, in what USA media reported was a possible hostage situation.
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