We have developed an approach to grow high quality ultra-thin films of La2-xSrxCuO4 with molecular beam epitaxy, by adding a homoepitaxial buffer layer in order to minimize the degradation of the film structure at the interface. The advantage of this method is to enable a further reduction of the minimal thickness of a superconducting La1.9Sr0.1CuO4 film. The main result of our work is that a single unit cell (only two copper oxide planes) grown on a SrLaAlO4 substrate exhibits a superconducting transition at 12.5 K (zero resistance) and an in-plane magnetic penetration depth lambda(ab)(0) = 535 nm.