A long-term goal for superconductors is to increase the superconducting transition temperature, T C. In cuprates, T C depends strongly on the out-of-plane Cu-apical oxygen distance and the in-plane Cu-O distance, but there has been little attention paid to tuning them independently. Here, in simply grown, self-assembled, vertically aligned nanocomposite thin films of La2CuO4+δ + LaCuO3, by strongly increasing out-of-plane distances without reducing in-plane distances (three-dimensional strain engineering), we achieve superconductivity up to 50 K in the vertical interface regions, spaced ~50 nm apart. No additional process to supply excess oxygen, e.g., by ozone or high-pressure oxygen annealing, was required, as is normally the case for plain La2CuO4+δ films. Our proof-of-concept work represents an entirely new approach to increasing T C in cuprates or other superconductors.