The high-temperature, all-inorganic CsPbI3 perovskite black phase is metastable relative to its yellow, nonperovskite phase at room temperature. Because only the black phase is optically active, this represents an impediment for the use of CsPbI3 in optoelectronic devices. We report the use of substrate clamping and biaxial strain to render black-phase CsPbI3 thin films stable at room temperature. We used synchrotron-based, grazing incidence, wide-angle x-ray scattering to track the introduction of crystal distortions and strain-driven texture formation within black CsPbI3 thin films when they were cooled after annealing at 330 degrees C. The thermal stability of black CsPbI3 thin films is vastly improved by the strained interface, a response verified by ab initio thermodynamic modeling.