Heavy Baryon Masses in the $1/m_Q$ and $1/N_c$ Expansions

The masses of baryons containing a single heavy quark are studied in a combined expansion in $1/m_Q$, $1/N_c$ and $SU(3)$ flavor symmetry breaking. Heavy quark baryon mass splittings are related to mass splittings of the octet and decuplet baryons. The $\Sigma_c^*$, $\Xi_c^\prime$ and $\Omega_c^*$ are predicted to the level of a few MeV. A number of bottom baryon mass splittings are predicted very accurately.