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

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... se states coincide with those in ordinary baryons in the large-N_c limit. The energy due to the gluon field is of order Λ_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.