The concept of electronic phase separation explains several unusual magnetic and electronic properties of doped perovskite oxides such as cuprates, manganites, and cobaltites. Strontium cobalt oxide with varying oxygen concentration (SrCoO_3-y, 0 < y < 0.125) is one of the systems which shows magnetic phase separation for intermediate oxygen values. The end points are SrCoO_2.875 which is ferromagnetic with T_c = 220 K and SrCoO₃ which is also ferromagnetic but with T_c = 280 K. Samples with intermediate values of oxygen concentration show two phase magnetic behavior between these values, but a single average structure as determined by diffraction. We undertook high resolution x-ray powder diffraction measurements to better understand the underlying structure. SrCoO₃ remains in the simple cubic perovskite structure from 10-300 K. SrCoO_2.875 has a much more complicated structure. At room temperature it is tetragonal with an expanded unit cell. Upon cooling, the structure appears to undergo a second order transition to a cubic phase. This is extremely unusual and the opposite of typical structural transitions which proceed to lower symmetry structures at lower temperatures. We present our structural studies and supporting DFT calculations of the energetics of the phases identified.