What is the identity of this fruit/tree found near Berkeley, California, USA?
Given that it's in central California, it's almost certainly California buckeye (Aesculus californica).  The tree is common in the Coast range and Sierra foothills of California.  It has adapted to the Mediterranean climate of the region by growing during the wet winter and spring and then dropping its leaves during the hot, dry summer.  The large seed is toxic if consumed.