  The hyperfine mass splittings of baryons containing a heavy quark are derived
at leading order in large $N$ QCD. Hyperfine splittings either preserve or
violate heavy quark spin symmetry. Previous work proves that the splittings
which preserve heavy quark spin symmetry are proportional to ${\bf J}^2$ at
order $1/N$, where $J$ is the angular momentum of the light degrees of freedom
of the baryon. This work proves that the splittings which violate heavy quark
spin symmetry are proportional to ${\bf J} \cdot {\bf S_Q}$ at order $1/(N
m_Q)$ in the $1/N$ and $1/m_Q$ expansions.
