© 2017. The American Astronomical Society. All rights reserved. Detecting the atmospheres of low-mass, low-temperature exoplanets is a high-priority goal on the path to ultimately detecting biosignatures in the atmospheres of habitable exoplanets. High-precision HST observations of several super-Earths with equilibrium temperatures below 1000 K have to date all resulted in featureless transmission spectra, which have been suggested to be due to high-altitude clouds. We report the detection of an atmospheric feature in the atmosphere of a 1.6 M⊕ transiting exoplanet, GJ 1132 b, with an equilibrium temperature of ∼600 K and orbiting a nearby M dwarf. We present observations of nine transits of the planet obtained simultaneously in the griz and JHK passbands. We find an average radius of 1.43 ±0.16 R⊕ for the planet, averaged over all the passbands, and a radius of 0.255 ±0.023 R⊙for the star, both of which are significantly greater than previously found. The planet radius can be decomposed into a "surface radius" at ∼1.375 R⊕ overlaid by atmospheric features that increase the observed radius in the z and K bands. The z-band radius is 4σ higher than the continuum, suggesting a strong detection of an atmosphere. We deploy a suite of tests to verify the reliability of the transmission spectrum, which are greatly helped by the existence of repeat observations. The large z-band transit depth indicates strong opacity from H2O and/or CH4 or a hitherto-unconsidered opacity. A surface radius of 1.375 ±0.16 R⊕ allows for a wide range of interior compositions ranging from a nearly Earth-like rocky interior, with ∼70% silicate and ∼30% Fe, to a substantially H2O-rich water world.