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The circularly polarized photogalvanic effect (CPGE) is studied in chiral Weyl semimetals with short-range quenched disorder. Without disorder, the topological properties of chiral Weyl semimetals lead to quantization of the CPGE, which is a second-order optical response. Using a combination of diagrammatic perturbation theory in the continuum and exact numerical calculations via the kernel polynomial method on a lattice model, we show that disorder perturbatively destabilizes the quantization of the CPGE.