Kaine was born at Saint Joseph's Hospital in St. Paul, Minnesota. He is the eldest of three sons born to Mary Kathleen (nee Burns), a home economics teacher, and Albert Alexander Kaine, Jr., a welder and the owner of a small iron-working shop. He was raised Catholic. One of Kaine's great-grandparents was Scottish and the other seven were Irish.

In 2005, Kaine ran for governor of Virginia against Republican candidate Jerry W. Kilgore, a former state attorney general. Kaine was considered an underdog for most of the race, trailing in polls for most of the election. Two polls released in September 2005 showed Kaine trailing Kilgore--by four percentage points in a Washington Post poll and by one percentage point in a Mason-Dixon/Roanoke Times poll. The final opinion polls of the race before the November election showed Kaine slightly edging ahead of Kilgore.  Kaine ultimately prevailed, winning 1,025,942 votes (51.7%) to Kilgore's 912,327 (46.0%). (A third candidate--independent state Senator H. Russell Potts Jr., who ran as an "independent Republican"--received 43,953 votes (2.2%)).  Kaine emphasized fiscal responsibility and a centrist message. He expressed support for controlling sprawl and tackling longstanding traffic issues, an issue that resonated in the exurbs of northern Virginia. He benefited from his association with the popular outgoing Democratic governor, Mark Warner, who had performed well in traditionally Republican areas of the state. On the campaign trail, Kaine referred to the "Warner-Kaine administration" in speeches and received the strong backing of Warner. Kilgore later attributed his defeat to Warner's high popularity and the "plummeting popularity" of Republican President George W. Bush, who held one rally with Kilgore on the campaign's final day.  The campaign turned sharply negative in its final weeks, with Kilgore running television attack ads that claimed, incorrectly, that Kaine believed that "Hitler doesn't qualify for the death penalty." The ads also attacked Kaine for his service ten years earlier as a court-appointed attorney for a death-row inmate. The Republican ad was denounced by the editorial boards of the Washington Post and a number of Virginia newspapers as a "smear" and "dishonest." Kaine responded with an ad "in which he told voters that he opposes capital punishment but would take an oath and enforce the death penalty. In later polls, voters said they believed Kaine's response and were angered by Kilgore's negative ads."  In the election, Kaine won by large margins in the Democratic strongholds such as Richmond and Northern Virginia's inner suburbs (such as Alexandria and Arlington), as well as in the Democratic-trending Fairfax County. Kaine also won Republican-leaning areas in Northern Virginia's outer suburbs, including Prince William County and Loudoun County, where George W. Bush had beat John Kerry in the previous year's presidential election, and performed "surprisingly well in Republican strongholds like Virginia Beach and Chesapeake." Kaine also defeated Kilgore in the burgeoning Richmond suburbs. Kilgore led in southwest Virginia and in the Shenandoah Valley.

Using a quote from the above article, answer the following question: Did he run for Governor?
Kaine ran for governor