Afghanistan, Nov. 12 -- Nvidia chief executive Jensen Huang is facing a second allegation of an extramarital relationship, this time with a senior company executive who reports directly to him. The allegation deepens a crisis that has already put his future at the chipmaker in doubt.

The New York Times reported on Wednesday that Huang, 63, had a relationship with Kimberly Powell, 48, Nvidia's vice president of health care. The newspaper cited five people who had worked at the company. It said both Huang and Powell are married to other people.

According to the Times, the two were filmed being affectionate at a San Jose hotel in March, during Nvidia's annual developer conference. When the paper reached Huang by phone and asked about Powell,...