I never noticed the tiny white flowers before. I always saw them before they opened and thought they were something else--what, I don't know. But I think that this is some sort of Osmanthus (Olive family, Oleaceae).
From the one book on shrubs I have, I have narrowed it down to Osmanthus fortunei--hybrid derived from O. fragrans and O. heterphyllus. But it says it blooms in the fall, and this is early summer. The leaves are finely toothed and the flowers appear in clusters of 7. This site, however, says the leaves are more sharply toothed. So maybe not. The search goes on.
There is a native species, O. americanus (Devilwood), but the leaves are longer and have no teeth.