oh, no, wait... That was in November 2000. ;-)

From MSNBC: " Schwarzenegger, who began his quest to be governor of California on late-night television, crafted a Hollywood ending to one of the most extraordinary political melodramas in the nation’s history.
In his victory speech Tuesday night, the 56-year-old action star offered to “extend the olive branch of political reconciliation” to his former opponents, and threw down a challenge to those comfortable with governmental gridlock: “For the people to win, politics as usual must lose.”
Schwarzenegger must work with Democrats, who are a majority of both houses in the Legislature and hold all statewide offices except his newly won governorship.
An Austrian-born immigrant who started life in America as a bodybuilder, Schwarzenegger said he intended to “call the leaders of the Legislature, and will let them know my door will always be open. ... I extend my hand to them. I need your help.”"

How long 'til he's the first non-Native born President? Less than a decade, I fancy. And in case my cynicism is not coming across in written form - I'm not happy about the prospect.