We present the structure of the interface responsible for epitaxy of crystalline oxides on silicon. Using synchrotron x-ray diffraction, we observe a 2 x 1 unit cell reconstruction at the interface of BaO grown on Si(001) terminated with 1/2 ML of Sr. Since this symmetry is not present in bulk BaO or Si, only the interface contributes to diffracted intensity. First principles calculations accurately predict the observed diffraction and identify the structure of the BaO/Si interface, including the elemental composition and a sub-A rumpling due to epitaxial strain of the 7 adjacent BaO and Si layers.