There are 3 levels of chain restrictions in California: R1, R2, and R3.
R1: Chains, traction devices, or snow tires required on the drive axle of all vehicles, except 4WD or AWD
R2: Chains, traction devices required for all vehicles except 4WD/AWD with snow tires.
R3: Chains or traction devices required for all vehicles.
“Snow Tires” includes all season radial tires (most autos come with them). That means that most autos need only put chains on in R2 conditions, and most AWD/4WD autos need only put chains on in R3 conditions. However, this is the legal minimum. It is a good idea to put them on anyway. Remember that 4WD/AWD does little or nothing to help you stop.
R3 conditions are rare. The CHP typically closes the road when conditions reach that point.
The speed limit under R1, R2, or R3 conditions is never more than 35 MPH. Even if you are on dry pavement, if you are going 35+ MPH under chain restrictions, you are risking a ticket.
You are advised to carry chains in your vehicle when entering the Sierra Nevada foothills and mountains from November 1st through May 1st.