We infer the mean optical depth of a sample of optically selected galaxy clusters from the Dark Energy Survey via the pairwise kinematic Sunyaev-Zel’dovich (KSZ) effect. The pairwise KSZ signal between pairs of clusters drawn from the Dark Energy Survey Year-3 cluster catalog is detected at 4.1σ in cosmic microwave background temperature maps from two years of observations with the SPT-3G camera on the South Pole Telescope. After cuts, there are 24,580 clusters in the ∼1,400 deg2 of the southern sky observed by both experiments. We infer the mean optical depth of the cluster sample with two techniques. The optical depth inferred from the pairwise KSZ signal is ¯τe = (2.97 ± 0.73) × 10−3, while that inferred from the thermal SZ signal is ¯τe = (2.51 ± 0.55stat ± 0.15 syst) ×10−3. The two measures agree at 0.6σ. We perform a suite of systematic checks to test the robustness of the analysis.