A variational calculation of the ground-state energy of liquid He3 is presented. The trial wave functions investigated are correlated pairing functions. By including pairing, we are able to investigate the possibility that the ground state of liquid He3 is pair condensed. The correlation permits us to apply the theory to a realistic model of the He3 interactions, including the strong short-range repulsion. The energy of a normal-state trial function is compared at several densities to the energy of singlet s-wave pair condensed state (BCS pairing) and the isotropic triplet pair condensed state (Balian-Werthamer pairing). Within the approximations used, the lowest-energy state from this class of trial functions is the normal state. We briefly discuss possible reasons for the failure of this calculation to exhibit the experimentally observed superfluid state.