Capitalizing on the observational advantage offered by its tiny M dwarf host, we present Hubble Space Telescope/Wide Field Camera 3 (WFC3) grism measurements of the transmission spectrum of the super-Earth exoplanet GJ1214b. These are the first published WFC3 observations of a transiting exoplanet atmosphere. After correcting for a ramp-like instrumental systematic, we achieve nearly photon-limited precision in these observations, finding the transmission spectrum of GJ1214b to be flat between 1.1 and 1.7{mu}m. Inconsistent with a cloud-free solar composition atmosphere at 8.2{sigma}, the measured achromatic transit depth most likely implies a large mean molecular weight for GJ1214b's outer envelope. A dense atmosphere rules out bulk compositions for GJ1214b that explain its large radius by the presence of a very low density gas layer surrounding the planet. High-altitude clouds can alternatively explain the flat transmission spectrum, but they would need to be optically thick up to 10 mbar or consist of particles with a range of sizes approaching 1 {mu}m in diameter.