The elusive β^{-}p^{+} decay was observed in ^{11}Be by directly measuring the emitted protons and their energy distribution for the first time with the prototype Active Target Time Projection Chamber in an experiment performed at ISAC-TRIUMF. The measured β^{-}p^{+} branching ratio is orders of magnitude larger than any previous theoretical model predicted. This can be explained by the presence of a narrow resonance in ^{11}B above the proton separation energy.