Organolead trihalide perovskites are shown to exhibit the best of both worlds: charge-carrier mobilities around 10 cm2 V−1 s−1 and low bi-molecular charge-recombination constants. The ratio of the two is found to defy the Langevin limit of kinetic charge capture by over four orders of magnitude. This mechanism causes long (micrometer) charge-pair diffusion lengths crucial for flat-heterojunction photovoltaics.