By Piya Sinha-Roy

LOS ANGELES (Reuters) - The parents of the late "Star Trek" movie actor Anton Yelchin sued Fiat Chrysler Automobiles NV <FCHA.MI> <FCAU.N> for negligence and product liability on Tuesday over the rollaway crash of a Jeep Grand Cherokee that killed their son.

The lawsuit, filed in Los Angeles County Superior Court, is believed to be the first wrongful death complaint linked to the Fiat Chrysler recall in April of more than 1.1 million cars and SUVs because of vehicles that roll away after drivers exit them.

Yelchin, 27, was killed on June 19 when his 2015 Grand Cherokee, which was covered under the recall, rolled backward in the steep driveway of his Los Angeles home and crushed the actor against a brick wall and fence.

The 18-page lawsuit points to a transmission gear-selector design it describes as "defective" as being the cause of numerous driverless rollaway mishaps like the one that killed Yelchin.

Gary Dordick, the attorney representing Yelchin's parents, said Fiat Chrysler had sent a recall letter to the actor that was received seven days after his death.

The undated letter addressed to Yelchin was displayed at the news conference and said "your vehicle may roll away, striking and injuring you, your passengers, or bystanders, if the vehicle's engine is left running, the parking brake is not engaged, and the transmission is not in the "PARK" position before exiting the vehicle."

Dordick said Yelchin had returned to his home on the evening of June 19 to pick up something he had forgotten and exited the car, "believing the vehicle to be in park."

The Russian-born actor, whose parents were both celebrated figure skaters in the former Soviet Union, was best known for playing the young starship navigator Pavel Chekov in the movie reboot of "Star Trek."

"In spite of our unbelievable grief, we decided to come here to prevent other families from the same tragedy," his father, Victor Yelchin, said in tearful remarks to reporters.

His wife, Irina Yelchin, said of her son, "He was very special, but now he's very special because his death might just save some other life."

The automaker said in a statement it had not been served with a lawsuit and declined to comment on it, but expressed its "sympathies to the Yelchin family for their tragic loss."

The U.S. National Highway Traffic Safety Administration (NHTSA) has said that the gear selectors in question clearly pose a safety issue that has led to hundreds of crashes and dozens of injuries.

The problem has been tied to at least 68 injuries, 266 crashes and 308 reports of property damage. Yelchin's death marked the first known fatality linked to the issue.

The recall applies to 811,000 vehicles in the United States, covering the 2014-2015 model years of the Jeep Grand Cherokee sport utility vehicle and 2012-2014 Dodge Charger and Chrysler 300 sedans.

Fiat Chrysler announced in June that it would soon furnish software upgrades to address the problem in all recalled vehicles.

(Additional reporting by David Shepardson in Traverse City, Michigan; Writing by Steve Gorman; Editing by Grant McCool and Jonathan Oatis)