  A recently discovered high-Tc cuprate superconductor Ba2CuO$_{4-\delta}$
exhibits exceptional Jahn-Teller distortion, wherein the CuO6 octahedrons are
compressed along the c axis. As a consequence, the O vacancies prefer to reside
in the CuO2 plane, but the exact structure is not known. By combining
first-principles total energy calculation with the automated structure
inversion method, the effective cluster interactions of O vacancies are mapped
out. Around $\delta$=0.8, where the 73K superconductivity was observed
experimentally, we predict that the ordered O vacancies slice the CuO2 plane
into not only 1D chains and but also two-leg ladders. A Monte Carlo simulation
is performed based on the effective cluster interaction model, showing that
such an ordering pattern is stable up to ~900 K. Our results put forth a
concrete structural basis to discuss the underlying superconducting mechanism.
