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 0.006Å −2 the system is a very dilute gas, that at that density is in equilibrium with a liquid of density 0.014Å −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.PACS numbers: 05.30. Fk, 67.30ej Recent heat capacity measurements of 3 He adsorbed on graphite by Sato et al. [1,2] have shown that its monolayer is a stable liquid in the density range 0.006-0.009Å −2 . One of the most interesting aspects of this phase is its extremely low density, with interparticle distances as large as 10Å, which could constitute one of the lowest-density stable liquids in nature. This new finding has re-opened an old issue that has been under discussion for more than thirty years, i.e., the nature (gas or liquid) of two-dimensional (2D) 3 He [3,4]. Previous experiments showed contradictory results due in part to the different setups and employed substrates [5][6][7][8]. Now, the new data from Ref.[1] on a clean graphite substrate seem to incline the debate towards the confirmation of this liquid phase existence.On the theoretical side, there is a broad consensus on the gas character of strictly 2D3 He [9-13]. However, the practical need of a substrate to actually realize the 3 He monolayer could modify this result. Previous attempts to calculate the properties of the adsorbed monolayer in a strongly attractive substrate such as graphite arrived to the same result. In Ref. [14], it is shown that the possibility of 3 He atoms moving perpendicularly to the surface leads to a stable liquid phase when the substrate is weakly attractive, as on some alkali metal surfaces. This is probably expected because the system goes from a 2D film to a three-dimensional (3D) configuration where liquid 3 He is the ground-state phase.In this work, we concerned ourselves with the adsorption of 3 He on a clean surface of graphite, trying to reproduce the recent experimental findings of Sato et al.[1] Our goal was to bridge the discrepancy between the strictly 2D calculations and the experimental data by improving the theoretical description of the system.Since considering a quasi-two dimensional flat adsorbent is clearly not enough for graphite [14], we included the effects of ...