In the present work, the electronic structure and chemical bonding of the MoC X3Σ- ground state and the six lowest excited states, A3Δ, a1Γ, b5Σ-, c1Δ, d1Σ+, and e5Π, have been investigated in detail using multireference configuration interaction methods and basis sets, including relativistic effective core potentials. In addition, scalar relativistic effects have been considered in the second order Douglas-Kroll-Hess approximation, while spin-orbit coupling has also been calculated. Five of the investigated states, X3Σ-, A3Δ, a1Γ, c1Δ, and d1Σ+, present quadruple σ2σ2π2π2 bonds. Experimentally, the predissociation threshold of MoC was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the dissociation energy of the ground state. Theoretically, the complete basis set limit of the calculated dissociation energy with respect to the atomic ground state products, including corrections for scalar relativistic effects, De(D0), is computed as 5.13(5.06) eV, in excellent agreement with our measured value of D0(MoC) of 5.136(5) eV. Furthermore, the calculated dissociation energies of the states having quadruple bonds with respect to their adiabatic atomic products range from 6.22 to 7.23eV. The excited electronic states A3Δ2 and c1Δ2 are calculated to lie at 3899 and 8057 cm-1, also in excellent agreement with the experimental values of DaBell et al., 4002.5 and 7834 cm-1, respectively.