  Recent heat-capacity experiments show quite unambiguously the existence of a
liquid $^3$He phase adsorbed on graphite. This liquid is stable at an extremely
low density, possibly one of the lowest found in Nature. Previous theoretical
calculations of the same system, and in strictly two dimensions, agree with the
result that this liquid phase is not stable and the system is in the gas phase.
We calculated the phase diagram of normal $^3$He adsorbed on graphite at $T=0$
using quantum Monte Carlo methods. Considering a fully corrugated substrate we
observe that at densities lower that 0.006 \AA$^{-2}$ the system is a very
dilute gas, that at that density is in equilibrium with a liquid of density
0.014 \AA$^{-2}$. Our prediction matches very well the recent experimental
findings on the same system. On the contrary, when a flat substrate is
considered, no gas-liquid coexistence is found, in agreement with previous
calculations. We also report results on the different solid structures, and the
corresponding phase transitions that appear at higher densities.
