Epitaxial thin films of the infinite-layer compounds SrCuO{sub 2} and CaCuO{sub 2} have been grown in a layer-by-layer mode on (100) SrTiO{sub 3} substrates by pulsed laser deposition with in situ monitoring using reflection high-energy electron diffraction (RHEED). While the pseudomorphic growth of SrCuO{sub 2} thin films on lattice-matched SrTiO{sub 3} substrates has been reported previously, we have also successfully synthesized for the first time high quality thin films of the other end-member, CaCuO{sub 2}, which is an important structural component of a number of cuprate superconductors. The stabilization of the infinite-layer CaCuO{sub 2} has been achieved by using an epitaxial layer of the infinite-layer SrCuO{sub 2} film as a chemical template for the nucleation and growth of this highly metastable phase. The oxygen concentration used during deposition and subsequent cooldown of the films has been observed to result in subtle structural modifications in the infinite-layer compounds, with substantial influence on their transport properties.