Fast03-then the rules are kinda mis leading from dot.ca.gov!
"California does not have any specific's when vehicles are required to carry chains. When the road is posted with a sign requiring chains, all heavy-duty vehicles (over 6,500 pounds gross weight) must be equipped with chains mounted on the tires in order to proceed. Depending on the severity of road conditions, some vehicles (passenger cars, 4-wheel drive vehicles with snow tires) may not be required to install chains at that point. The exceptions will be posted on the sign."
Then they say
"If I have 4-wheel-drive, do I need to carry chains?
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."