The unique inner-belt asteroid 311P/PANSTARRS (formerly P/2013 P5) is notable for its sporadic, comet-like ejection of dust in nine distinct epochs spread over $sim$250 days in 2013. This curious behavior has been interpreted as the product of localized, equator-ward landsliding from the surface of an asteroid rotating at the brink of instability. We obtained new Hubble Space Telescope observations to directly measure the nucleus and to search for evidence of its rapid rotation. However, instead of providing photometric evidence for rapid nucleus rotation, our data set a lower limit to the lightcurve period, $P ge$ 5.4 hour. The dominant feature of the lightcurve is a V-shaped minimum, $sim$0.3 magnitudes deep, that is suggestive of an eclipsing binary. Under this interpretation, the time-series data are consistent with a secondary/primary mass ratio, $m_s/m_p sim$ 1:6, a ratio of separation/primary radius, $r/r_p sim$ 4 and an orbit period $sim$0.8 days. These properties lie within the range of other asteroid binaries that are thought to be formed by rotational breakup. While the lightcurve period is long, centripetal dust ejection is still possible if one or both components rotates rapidly ($lesssim$ 2 hour) and has a small lightcurve variation because of azimuthal symmetry. Indeed, radar observations of asteroids in critical rotation reveal muffin-shaped morphologies which are closely azimuthally symmetric and which show minimal lightcurves. Our data are consistent with 311P being a close binary in which one or both components rotates near the centripetal limit. The mass loss in 2013 suggests that breakup occurred recently and could even be on-going. A search for fragments that might have been recently ejected beyond the Hill sphere reveals none larger than effective radius $r_e sim$ 10 m.
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