Dark photons that kinetically mix with the Standard Model photon give rise to new spectral anisotropies (patchy dark screening) in the cosmic microwave background (CMB) due to conversion of photons to dark photons within large-scale structure. We utilize predictions for this patchy dark screening signal to provide the tightest constraints to date on the dark photon kinetic mixing parameter [ϵ≲4.5×10^{-8} (95% confidence level)] over the mass range 10^{-13} eV≲m_{A^{'}}≲10^{-11} eV, almost an order of magnitude stronger than previous limits, by applying state-of-the-art component separation techniques to the cross-correlation of Planck CMB and unWISE galaxy survey data.