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 ∼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 Teff ≃ 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.