The potential energy curve of e(+)LiH has been computed by means of diffusion Monte Carlo using explicitly correlated trial wave functions. This curve allows us to compute the adiabatic total and binding energies and the vibrational spectrum of e(+)LiH, and the adiabatic positron affinity of LiH. Using these results, we discuss the possibility to detect spectroscopically e(+)LiH in the gas phase, in order to have the first direct observation of a positron-containing system.