We investigate the properties of a system of He4 atoms at the absolute zero of temperature interacting via a Lennard-Jones potential, and constrained to motion in two dimensions by an otherwise inert substrate. Results of a semiclassical calculation indicate that the ground state is that of a self-bound liquid. It further indicates that a close-packed-solid configuration is not self-bound. A quantum-mechanical variational calculation is performed to obtain an upper bound on the energy of the system. A result of -0.61 A°K per particle is obtained at a density of 0.035 A-2. The relationship between this calculation and recent experiments on He4 monolayers is briefly discussed.