We present a mass map reconstructed from weak gravitational lensing shear measurements over 139 deg2 from the Dark Energy Survey science verification data. The mass map probes both luminous and dark matter, thus providing a tool for studying cosmology. We find good agreement between the mass map and the distribution of massive galaxy clusters identified using a red-sequence cluster finder. Potential candidates for superclusters and voids are identified using these maps. We measure the cross-correlation between the mass map and a magnitude-limited foreground galaxy sample and find a detection at the 6.8σ level with 20 arc min smoothing. These measurements are consistent with simulated galaxy catalogs based on N-body simulations from a cold dark matter model with a cosmological constant. This suggests low systematics uncertainties in the map. We summarize our key findings in this Letter; the detailed methodology and tests for systematics are presented in a companion paper.