  We study the properties and couplings of hybrid baryons in the large-$N_c$
expansion. These are color-neutral baryon states which contain in addition to
$N_c$ quarks also one constituent gluon. Hybrid baryons with both symmetric and
mixed symmetric orbital wave functions are considered. We introduce a Hartree
description for these states, similar to the one used by Witten for ordinary
baryons. It is shown that the Hartree equations for $N_c (N_c-1)$ quarks for
symmetric (mixed symmetric) states in these states coincide with those in
ordinary baryons in the large-$N_c$ limit. The energy due to the gluon field is
of order $\Lambda_{QCD}$. Under the assumption of color confinement, our
results prove the existence of hybrid baryons made up of heavy quarks in the
large $N_c$ limit and provides a justification for the constituent gluon
picture of these states. The couplings of the hybrid baryons to mesons of
arbitrary spin are computed in the quark model. Using constraints from the
large $N_c$ scaling laws for the meson-baryon scattering amplitudes, we write
down consistency conditions for the meson couplings of the hybrid baryons.
These consistency conditions are solved explicitly with results in agreement
with those in the quark model for the respective couplings.
