Steve Mollenkopf, CEO of Qualcomm at the Mobile World Congress in Barcelona on Feb. 23, 2016.

Qualcomm has obtained a permit to test autonomous vehicles on public roads in California, the latest step in the chipmaker's effort to gain a foothold in the self-driving car market.

California's Department of Motor Vehicles issued the permit, which authorizes testing for one vehicle and three drivers, on Dec. 12, a spokesperson from the agency told CNBC in an email.

"We certainly expect to be a key player in the autonomous space," Nakul Duggal, Qualcomm's vice president of product management for automotive, said in an interview. He declined to talk about forthcoming products that could enable autonomous driving.

In September Qualcomm announced the 9150 C-V2X chipset, which lets cars communicate with other cars as well as infrastructure like traffic lights. That technology could work alongside chips dedicated to autonomy by improving safety, Duggal said.

Qualcomm has begun field trials of Ford vehicles containing the chipsets in San Diego County, where the company is based, Duggal said. Similar tests of the technology will take place in Michigan, China, Germany, Italy and Japan, he said.

Nvidia picked up a permit to test self-driving cars in California just over a year ago, and earlier this year Samsung received a permit from the state. Nvidia has several automotive partners, including Tesla, Toyota and Volvo. Intel has expressed interest in autonomous driving but doesn't have a California self-driving permit.

Qualcomm technology is currently employed for telematics and infotainment systems. Last year the company announced a plan to acquire NXP, which sells several automotive components. The deal has not closed. In November Broadcom said it wanted to acquire Qualcomm for more than $100 billion, a proposal that Qualcomm's board rejected.