(FORTUNE Magazine) – Sara Lee's CEO runs a public company, but this summer he's been embroiled in a scandal involving a very private matter. In late July, Brenda Jarvis, 35, filed a sexual-discrimination lawsuit against Sara Lee's chief executive, C. Steven McMillan, and the $20 billion packaged-goods company, alleging that the CEO had offered her a job, then rescinded after she declined to continue a sexual relationship.

McMillan's plight is unusual. While high-profile sex scandals do occur in corporate America, more often than not CEO dalliances don't make headlines, and legal matters are usually settled behind closed doors. In Sara Lee's case, the company balked at attempts to settle privately, according to Jarvis's lawyer, Martin Oberman. Instead Sara Lee, which owns several brands that cater to female consumers--Playtex, L'Eggs hosiery, and Wonderbra among them--now plans to defend McMillan in what's sure to be a nasty courtroom dust-up. A court date is set for Aug. 27.

Although no one's placing bets on who will win the case, what's certain is that neither side can emerge untarnished. According to Jarvis's version of events, laid out in court documents, she met McMillan in early July 2003 at a social gathering in Palm Beach hosted by McMillan's daughter. The two discussed Jarvis's ongoing job hunt, after which McMillan said he might have a position for her. He offered Jarvis his business card and weeks later called her and asked that she come to Chicago for a weekend job interview. In her lawsuit are copies of her travel arrangements, made by Sara Lee's travel department (the company says McMillan paid for the trip with his personal AmEx). Jarvis's lawyer Oberman contends that this sort of unorthodox interview is a staple of executive-level business, and if she were a man invited to a country club to play golf over the weekend, it would never raise eyebrows. "Is there not a lot of business done at dinner clubs and golf courses?"

Once in Chicago, Jarvis was chauffeured in a company-owned car to a corporate apartment. That evening she met McMillan and two Sara Lee employees in a restaurant. Sometime after dinner, Jarvis says, McMillan offered her a $140,000-a-year marketing job at Sara Lee's Hanes division. Though nothing in writing was exchanged, she accepted. Later that weekend McMillan and Jarvis had sex. According to Jarvis, when she returned home to Dallas, McMillan asked her to accompany him on a business trip to Italy. She declined and informed him that she wanted their relationship to be strictly professional and not sexual. At that point, claims Jarvis, McMillan reneged on the job offer.

Jarvis's lawsuit also claims that McMillan defamed her, telling mutual friends and his daughter that Jarvis came to Chicago uninvited and was stalking him, demanding sex. McMillan's version of events differs largely in that he claims never to have offered Jarvis a job. "They spent the weekend together and had a one-night stand. It was purely social," says Sara Lee spokesperson Julie Ketay. "The allegations regarding potential employment at the company are completely fabricated." McMillan declined to comment.

McMillan, 58, is a twice-divorced single man who for years has carried a reputation as a bold bon vivant. It's the same attitude that aided his rise, managing various business operations in his 28 years with Sara Lee. During the 1980s, McMillan led the company's mergers and acquisitions team, negotiating hardnosed deals that led to Sara Lee's purchase of several European brands. During the 1990s, according to several former company executives, Sara Lee's human resources department warned McMillan that his public partying might interfere with his ambitions to succeed then-CEO John Bryan. By all accounts McMillan faded from the Chicago nightclub scene. He was named CEO in 2000.

Since then McMillan's performance as CEO has been mediocre. He has cut costs and streamlined the company's more than 200 food, apparel, and household brands, like Ball Park hot dogs and Champion sportswear, but even so, Sara Lee's operating income has declined in three of the past four years. "They've had numerous expensive restructurings with nothing to show for it," says Marina Vendrova, a food analyst with Edward Jones, a St. Louis research firm. Nevertheless, McMillan's job appears secure--at least in the near future. His heir apparent, chief operating officer Brenda Barnes, 50, just joined the company on July 1. As for McMillan's sex case, the board stands behind him, having ordered an investigation of the matter themselves, according to board member Richard L. Thomas. "After a careful review of the facts," says Thomas, "the independent investigation concluded that the allegations made regarding potential employment at Sara Lee were completely false." --John Simons