We report the first observation of the Xe108→Te104→Sn100 α-decay chain. The α emitters, Xe108 [Eα=4.4(2) MeV, T1/2=58-23+106 μs] and Te104 [Eα=4.9(2) MeV, T1/2<18 ns], decaying into doubly magic Sn100 were produced using a fusion-evaporation reaction Fe54(Ni58,4n)Xe108, and identified with a recoil mass separator and an implantation-decay correlation technique. This is the first time α radioactivity has been observed to a heavy self-conjugate nucleus. A previous benchmark for study of this fundamental decay mode has been the decay of Po212 into doubly magic Pb208. Enhanced proton-neutron interactions in the N=Z parent nuclei may result in superallowed α decays with reduced α-decay widths significantly greater than that for Po212. From the decay chain, we deduce that the α-reduced width for Xe108 or Te104 is more than a factor of 5 larger than that for Po212.