Basically Caltrans/CHP would close the road before requiring 4WD to put on chains, but they may require you to at least have then with you, but the chances of you actually having to put them on are slim. As chuckH suggested - go to Walmart (or similar) and pick up a set for your rear axle - bring them - if you don't use them - just return it when you get back.

Everytime I have gone from the Bay Area to the Tahoe area - I have never been stopped - they just see an SUV and wave me by. They don't even check to see that I'm 4WD or if I have good treads left on my tires.