We report on a new metal halide perovskite photovoltaic cell that exhibits both very high solar-to-electric power-conversion efficiency and intense electroluminescence. We produce the perovskite films in a single step from a solution containing a mixture of FAI, PbI2, MABr, and PbBr2 (where FA stands for formamidinium cations and MA stands for methylammonium cations). Using mesoporous TiO2 and Spiro-OMeTAD as electron- and hole-specific contacts, respectively, we fabricate perovskite solar cells that achieve a maximum power-conversion efficiency of 20.8% for a PbI2/FAI molar ratio of 1.05 in the precursor solution. Rietveld analysis of x-ray diffraction data reveals that the excess PbI2 content incorporated into such a film is about 3 weight percent. Time-resolved photoluminescence decay measurements show that the small excess of PbI2 suppresses nonradiative charge carrier recombination. This in turn augments the external electroluminescence quantum efficiency to values of about 0.5%, a record for perovskite photovoltaics approaching that of the best silicon solar cells. Correspondingly, the open-circuit photovoltage reaches 1.18 V under AM 1.5 sunlight.