The alpha decay parameter in the process Omega-minus -> Lambda + K-minus has been measured from a sample of 4.50 million unpolarized Omega-minus decays recorded by the HyperCP (E871) experiment at Fermilab and found to be [1.78 +/- 0.19(stat) +/- 0.16(syst)]{times}10^{-2}. This is the first unambiguous evidence for a nonzero alpha decay parameter, and hence parity violation, in the Omega-minus -> Lambda + K-minus decay.