We present results of a stellar occultation by the Jupiter Trojan asteroid Patroclus and its nearly equal size moon, Menoetius. The geocentric mid-time of the event was 2013 October 21 06:43:02 UT. Eleven sites out of 36 successfully recorded an occultation. Seven chords across Patroclus yielded an elliptical limb fit of 124.6 by 98.2 km. There were six chords across Menoetius that yielded an elliptical limb fit of 117.2 by 93.0 km. There were three sites that got chords on both objects. At the time of the occultation we measured a separation of 664.6 km (0.247 arcsec) and a position angle for Menoetius of 2657 measured eastward from J2000 north. Combining this occultation data with previous light curve data, the axial ratios of both objects are 1.3 : 1.21 : 1, indicative of a mostly oblate ellipsoid with a slight asymmetry in its equatorial projection. The oblate shape is not an equilibrium shape for the current rotation period, but would be if it were rotating with an ~8 h period. This faster period is consistent with a pre-evolved state of the system with an orbital separation that is 50% smaller. Our best estimate of the system density is 0.88 g cm?3.
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