Long, balanced electron and hole diffusion lengths greater than 100 nanometers in the polycrystalline organolead trihalide compound CH3NH3PbI3 are critical for highly efficient perovskite solar cells. We found that the diffusion lengths in CH3NH3PbI3 single crystals grown by a solution-growth method can exceed 175 micrometers under 1 sun (100 mW cm(-2)) illumination and exceed 3 millimeters under weak light for both electrons and holes. The internal quantum efficiencies approach 100% in 3-millimeter-thick single-crystal perovskite solar cells under weak light. These long diffusion lengths result from greater carrier mobility, longer lifetime, and much smaller trap densities in the single crystals than in polycrystalline thin films. The long carrier diffusion lengths enabled the use of CH3NH3PbI3 in radiation sensing and energy harvesting through the gammavoltaic effect, with an efficiency of 3.9% measured with an intense cesium-137 source.