SAN FRANCISCO — Over 28 years at the giant computer chip maker Intel, Renée James climbed to its No. 2 position, becoming one of Silicon Valley’s prominent female leaders.

Now she is taking aim at Intel’s most lucrative business, one that she helped build.

Ms. James, who announced in 2015 that she would resign from Intel, on Monday revealed a start-up backed by the private equity firm Carlyle Group to sell chips to handle calculations in servers. Those computers run most internet services and corporate back-office operations.

Intel dominates that market, accounting for 98 percent of the microprocessor chips sold for the most popular variety of server, the research firm IDC estimates. The group that sells such chips generated about $19 billion in revenue last year and nearly half of Intel’s operating profit.

Ms. James emphasized her respect for her former employer and played down potential competition. She said her new company, Ampere, was designing chips for new, specialized jobs at cloud services that aren’t Intel’s primary focus.