We report the first observation of the ^{108}Xe→^{104}Te→^{100}Sn α-decay chain. The α emitters, ^{108}Xe [E_{α}=4.4(2) MeV, T_{1/2}=58_{-23}^{+106} μs] and ^{104}Te [E_{α}=4.9(2) MeV, T_{1/2}<18 ns], decaying into doubly magic ^{100}Sn were produced using a fusion-evaporation reaction ^{54}Fe(^{58}Ni,4n)^{108}Xe, 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 ^{212}Po into doubly magic ^{208}Pb. 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 ^{212}Po. From the decay chain, we deduce that the α-reduced width for ^{108}Xe or ^{104}Te is more than a factor of 5 larger than that for ^{212}Po.