  We have developed an approach to grow high quality ultrathin films of
La$_{2-x}$Sr$_x$CuO$_{4}$ 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
La$_{1.9}$Sr$_{0.1}$CuO$_{4}$ film. The main result of our work is that a
single unit cell (only two copper oxide planes) grown on a SrLaAlO$_4$
substrate exhibits a superconducting transition at 12.5 K (zero resistance) and
an in-plane magnetic penetration depth $\lambda_{ab}(0)$ = 535 nm.
