We present a potential explanation for the strain-induced metal-insulator transition that has recently been observed in thin films of SrCrO₃ using density-functional theory (DFT) and its extension to DFT+U. Our calculations show that the unstrained system exhibits a C-type antiferromagnetically ordered ground state, which is near to a Jahn-Teller instability, given realistic values of the Hubbard U parameter. However, the significant energy overlap between the higher-lying dxy band and the dxz/dyz band works against the JT distortion's. When epitaxially strained, this overlap is reduced by the lowering of the dxyband relative to dxz/dyz as the system gets closer to the nominal integer filling. The degeneracy between the dxz and dyz orbitals is subsequently lifted by the JT distortion, opening a gap in the electronic band structure.