  We present the discovery of a transiting exoplanet candidate in the K2
Field-1 with an orbital period of 9.1457 hr: K2-22b. The highly variable
transit depths, ranging from $\sim$0\% to 1.3\%, are suggestive of a planet
that is disintegrating via the emission of dusty effluents. We characterize the
host star as an M-dwarf with $T_{\rm eff} \simeq 3800$ K. We have obtained
ground-based transit measurements with several 1-m class telescopes and with
the GTC. These observations (1) improve the transit ephemeris; (2) confirm the
variable nature of the transit depths; (3) indicate variations in the transit
shapes; and (4) demonstrate clearly that at least on one occasion the transit
depths were significantly wavelength dependent. The latter three effects tend
to indicate extinction of starlight by dust rather than by any combination of
solid bodies. The K2 observations yield a folded light curve with lower time
resolution but with substantially better statistical precision compared with
the ground-based observations. We detect a significant "bump" just after the
transit egress, and a less significant bump just prior to transit ingress. We
interpret these bumps in the context of a planet that is not only likely
streaming a dust tail behind it, but also has a more prominent leading dust
trail that precedes it. This effect is modeled in terms of dust grains that can
escape to beyond the planet's Hill sphere and effectively undergo `Roche lobe
overflow,' even though the planet's surface is likely underfilling its Roche
lobe by a factor of 2.
