Yes. You will need to carry tire chains in your vehicle from November 1 to April 30 whether or not you actually use them. When CalTrans calls for chain restrictions, you will need to adhere to chain requirements. See Question 12 for levels of chain control.
"As defined in Section 605 of the California Vehicle Code (CVC), tire traction devices are designed to improve vehicle traction, braking, and cornering upon snow or ice-covered surfaces."
Road conditions and chain restrictions can be found on the Caltrans Quickmaps website. It is recommended that you stay up to date with road conditions as they can change quickly and without warning. Check all boxes under Options then Road Conditions for complete info.