The energy and two-photon annihilation rate of the complex of the LiH molecule with a positron have been calculated for the equilibrium geometry of LiH in the gas phase, using the explicitly correlated Gaussian basis set. The resulting energy of e(+)LiH (-8.104 850 hartree) is the lowest obtained to date. The binding energy of the positron in this system has been predicted to be at least 34.401 mhartree, and the annihilation rate has been estimated to be 1.26 ns(-1). Maps of the electron, positron, and contact (electron-positron) densities have been prepared.