Yes carry chains unless you have 4x4 with snow tires. There are retailers along the way that will sell you chains for a fair price, as I assume they will be hard to find in Berkeley. If your going right now I would not worry about chains there is no snow forecast for at least a week.
It's always a great idea to carry snow chains for your car any time you go to the mountains during the winter months. But right now you would not have to use them. Please be careful driving. Safe travels!
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