  Quantum Monte Carlo simulations at zero temperature of a $^3$He monolayer
adsorbed on graphite, either clean or preplated with $^4$He, unexpectedly point
to a gas-liquid phase transition at a very low areal density of the order of
0.01\AA$^{-2}$. This result stems from an essentially unbiased calculation of
the ground state energy for an infinite, defect-free substrate which interacts
with He atoms via a realistic potential, whereas the interaction between two He
atoms includes two- and three-body terms. The sensitivity of the gas-liquid
coexistence region on the model Hamiltonian employed is discussed.
