Resonance spectral lines such as H I Ly {alpha}, Mg II h&k, and Ca II H&K that form in the solar chromosphere are influenced by the effects of 3D radiative transfer as well as partial redistribution (PRD). So far no one has modeled these lines including both effects simultaneously owing to the high computing demands of existing algorithms. Such modeling is however indispensable for accurate diagnostics of the chromosphere. We present a computationally tractable method to treat PRD scattering in 3D model atmospheres using a 3D non-LTE radiative transfer code. To make the method memory-friendly, we use the hybrid approximation of Leenaarts et al. (2012) for the redistribution integral. To make it fast, we use linear interpolation on equidistant frequency grids. We verify our algorithm against computations with the RH code and analyze it for stability, convergence, and usefulness of acceleration using model atoms of Mg II with the h&k lines and H I with the Ly {alpha} line treated in PRD. A typical 3D PRD solution can be obtained in a model atmosphere with $252 times 252 times 496$ coordinate points in 50 000--200 000 CPU hours, which is a factor ten slower than computations assuming complete redistribution. We illustrate the importance of the joint action of PRD and 3D effects for the Mg II h&k lines for disk-center intensities as well as the center-to-limb variation. The proposed method allows simulating PRD lines in time series of radiation-MHD models in order to interpret observations of chromospheric lines at high spatial resolution.
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