The stability and spontaneous decay of naturally occurring atomic nuclei have been much studied ever since Becquerel discovered natural radioactivity in 1896. In 1960, proton-rich nuclei with an odd or an even atomic number Z were predicted to decay through one- and two-proton radioactivity, respectively. The experimental observation of one-proton radioactivity was first reported in 1982, and two-proton radioactivity has now also been detected by experimentally studying the decay properties of 45Fe (refs 3, 4) and 54Zn (ref. 5). Here we report proton-proton correlations observed during the radioactive decay of a spinning long-lived state of the lightest known isotope of silver, 94Ag, which is known to undergo one-proton decay. We infer from these correlations that the long-lived state must also decay through simultaneous two-proton emission, making 94Ag the first nucleus to exhibit one- as well as two-proton radioactivity. We attribute the two-proton emission behaviour and the unexpectedly large probability for this decay mechanism to a very large deformation of the parent nucleus into a prolate (cigar-like) shape, which facilitates emission of protons either from the same or from opposite ends of the 'cigar'.