We present Atacama Large Millimeter/Submillimeter Array (ALMA) observations of a wide binary system in Orion, with projected separation 440?AU, in which we detect submillimeter emission from the protoplanetary disks around each star. Both disks appear moderately massive and have strong line emission in CO 3-2, HCO+ 4-3, and HCN 3-2. In addition, CS 7-6 is detected in one disk. The line-to-continuum ratios are similar for the two disks in each of the lines. From the resolved velocity gradients across each disk, we constrain the masses of the central stars, and show consistency with optical-infrared spectroscopy, both indicative of a high mass ratio ~9. The small difference between the systemic velocities indicates that the binary orbital plane is close to face-on. The angle between the projected disk rotation axes is very high, ~72°, showing that the system did not form from a single massive disk or a rigidly rotating cloud core. This finding, which adds to related evidence from disk geometries in other systems, protostellar outflows, stellar rotation, and similar recent ALMA results, demonstrates that turbulence or dynamical interactions act on small scales well below that of molecular cores during the early stages of star formation.
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