The decay of extremely neutron-deficient 45Fe has been studied in detail by means of a novel type of a gaseous detector employing digital imaging to record tracks of charged particles. The two-proton radioactivity channel was clearly identified. For the first time, the angular and energy correlations between two protons emitted from the nuclear ground state were determined, indicating the genuine three-body character of this decay. The half-life of 45Fe was found to be 2.6+/-0.2 ms and the observed 2p decay branching ratio is 70+/-4%.