We report the result of the search for neutrinoless double beta decay of ^{82}Se obtained with CUPID-0, the first large array of scintillating Zn^{82}Se cryogenic calorimeters implementing particle identification. We observe no signal in a 1.83 kg yr ^{82}Se exposure, and we set the most stringent lower limit on the 0νββ ^{82}Se half-life T_{1/2}^{0ν}>2.4×10^{24} yr (90% credible interval), which corresponds to an effective Majorana neutrino mass m_{ββ}<(376-770) meV depending on the nuclear matrix element calculations. The heat-light readout provides a powerful tool for the rejection of α particles and allows us to suppress the background in the region of interest down to (3.6_{-1.4}^{+1.9})×10^{-3} counts/(keV kg yr), an unprecedented level for this technique.