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 onu $^{82}$Se half-life T$^{0 u}_{1/2}>$ 2.4$times mathrm{10}^{24}$ yr (90% credible interval), which corresponds to an effective Majorana neutrino mass m$_{betabeta} <$ (376-770) meV depending on the nuclear matrix element calculations. The heat-light readout provides a powerful tool for the rejection of al particles and allows to suppress the background in the region of interest down to (3.6$^{+1.9}_{-1.4}$)$times$10$^{-3}$ckky, an unprecedented level for this technique.
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