Do I need chains driving on I-80 through Tahoe in June?

Okay, I've never really taken a road trip out of California before and I'm not sure when it's snowing other places or not. I'm driving from Oakland, CA to Reno, NV in late June. I'll be going up I-5 then taking I-80 through Tahoe National Forest to get to Reno. Is there a possibility I might need chains in late June?