For the sake of getting a definitive answer, I did some web searching and found this on the CHP website.
http://www.chp.ca.gov/html/answers.html
I have a 4-wheel drive vehicle. Do I have to carry / use chains? What do the "R" ratings which are associated with chain requirements mean?
"R" ratings on snowy roads indicate chain requirements for various conditions. Some vehicles may not be required to use chains under all conditions, but
all vehicles must carry chains. Most vehicles come equipped with snow tires. Look for M+S (mud and snow), All Season, or All Terrain, on the side of the tire.
R-1 chains required except for vehicles with snow tires (chains required for any vehicle pulling a trailer)
R-2 chains required except for 4-wheel drive with snow tires
R-3 chains required for all vehicles
As well as this on the CA Department of Transportation website.
http://www.dot.ca.gov/hq/traffops/trucks/ops-guide/chains.html
If I have 4-wheel-drive, do I need to carry chains?
Yes. Even though weather conditions may not warrant the use of chains on 4-wheel-drive vehicles at a particular time, to enter a chain control area, you must have a set of chains (for one drive axle) for your vehicle in your possession. If conditions worsen or you have trouble controlling your vehicle, you must stop and install the chains.