  We present a calculation of the charmonium spectrum with three flavors of
dynamical staggered quarks from gauge configurations that were generated by the
MILC collaboration. We use the Fermilab action for the valence charm quarks.
Our calculation of the spin-averaged 1P--1S and 2S--1S splittings yields a
determination of the strong coupling, with $\ams(M_Z) = 0.119 (4)$.
