In the field of high-temperature superconductivity there has been no increase in the critical temperature Tc of bulk compounds since 1993. However, an analysis of the uniaxial strain or pressure derivatives of Tc in the cuprate superconductors allows us to predict that under a compressive epitaxial strain, a large increase of Tc should be possible. We demonstrate the experimental feasibility of this approach for La2-xSrxCuO4±δ (214") thin films deposited on (001)-oriented SrLaAlO4 substrates for different Sr content (0.045 ≤ x ≤ 0.11). Under epitaxial strain, a large jump of the critical temperature Tc is observed, as well as a drastic change in the resistive behavior from insulating to metallic at low temperatures.