The layered lithium borocarbide LiBC, isovalent with and structurally similar to the superconductor MgB2, is an insulator due to the modulation within the hexagonal layers (BC vs. B2). We show that hole-doping of LiBC results in Fermi surfaces of B-C p sigma character that couple very strongly to B-C bond stretching modes, precisely the features that lead to superconductivity at Tc = 40 K in MgB2. Comparison of Li{0.5}BC with MgB2 indicates the former to be a prime candidate for electron-phonon coupled superconductivity at substantially higher temperature than in MgB2.