The experimentally unknown molecule ZnC has been studied using multireference methods in conjunction with quantitative basis sets. Full potential energy curves have been constructed for the ground (X(3)Sigma(-)) state and 29 excited states, focusing mainly on dissociation energies and bonding mechanisms. The X(3)Sigma(-) state of ZnC has a binding energy of 26.1 kcal/mol at the internally contracted multireference- (valence) configuration interaction level of theory (MRCI), whereas this value reduces to 23.3 kcal/mol upon including core-valence correlation effects (3d(10) of Zn) plus one-electron Douglas-Kroll relativistic corrections.