And it is big indeed, given that the storied Silicon Valley company has lurched from chief to chief to chief ever since the board, in 1999, eased out Lew Platt and recruited Carly Fiorina from Lucent .

Fiorina was the first No. 1 on the Fortune Most Powerful Women list, at the top from 1998 to 2004. Who grabbed the MPW crown from Fiorina? Whitman, when she was CEO of eBay .

H-P’s board fired Fiorina in early 2005 and has had a thing about women since. In 2006 came the removal of HP board chair Pattie Dunn. Then Mark Hurd, Fiorina’s CEO successor, got into trouble over his relationship with a female HP consultant. With Hurd’s 2010 ouster came new chief Leo Apotheker from SAP –and an influx of women to fill board seats and help clean up the mess.

Whitman, 55, was one of those new HP directors, fresh off her defeat in the California governor race. I hear that Whitman, who is also on the Procter & Gamble board, was key during the past couple of months as the board assessed Apotheker’s poor performance. Having taken a part-time gig at Kleiner Perkins Caufield & Byers last spring, to test her venture-capital chops, Whitman was available to step up. And ready. Fellow HP board member–and Kleiner partner–Ray Lane and another well-known VC, Marc Andreessen, apparently were critical in getting consensus among the directors.

Debate will rage about whether Whitman is right for the job. After building eBay from a startup to a Fortune 500 company, she stumbled toward the end of her CEO run.

The other question: Why would Whitman take this very difficult job? Having spent many days with Whitman (reporting Fortune cover stories about her in 2004 and 2009), I have a sense: A corporate strategist and manager to the core, she was trained at P&G and Disney and Bain Consulting, pre-eBay, and has long loved a giant management challenge. Also, having already gotten her head around the idea of running California, she probably didn’t think the H-P challenge is as daunting as other execs might.

So, now Meg Whitman is in charge of California’s second-largest company–behind Chevron . And HP is, six years after Carly, once again the largest Fortune 500 company led by a woman.

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