In an experiment at the SISSI-LISE3 facility of GANIL, the decay of the proton drip line nucleus 45Fe has been studied. Fragment-implantation events have been correlated with radioactive decay events in a 16x16 pixel silicon-strip detector. The decay-energy spectrum of 45Fe implants shows a distinct peak at (1.14+/-0.04) MeV with a half-life of T(1/2)=(4.7(+3.4)(-1.4)) ms. None of the events in this peak is in coincidence with beta particles. For a longer correlation interval, daughter decays of the two-proton daughter 43Cr can be observed after 45Fe implantation. The decay energy for 45Fe agrees nicely with several theoretical predictions for two-proton radioactivity.