The stochastic variational method (SVM) has been used to confirm the prediction of a quantum Monte Carlo (QMC) calculation (Bressanini et al 1998 J. Chem. Phys. 109 1716) that a positron can be bound to the lithium hydride molecule (LiH). The adiabatic approximation was not made and the nuclear motion was explicitly included in the calculation. A completely ab initio calculation gave a positron binding energy of 0.613 eV and constitutes an explicit demonstration of binding not restricted to the Born-Oppenheimer approximation. The fixed-core variant of the SVM was also used with a Li+ 1s2 core. The positron binding energy in the fixed-core SVM was 0.909 eV, which is approximately the same as that previously reported in the QMC calculation. The mean inter-nuclear radius was 3.96 a0 and the 2γ annihilation rate of the e+LiH ground state was 1.64×109 s-1.