Context. 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. Aims. We present a computationally tractable method to treat PRD scattering in 3D model atmospheres using a 3D non-local thermodynamic equilibrium (non-LTE) radiative transfer code. Methods. To make the method memory-friendly, we use the hybrid approximation for the redistribution integral. To make the method 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 i i with the h&k lines and H i with the Ly alpha line treated in PRD. Results. A typical 3D PRD solution can be obtained in a model atmosphere with 252 x 252 x 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. Conclusions. The proposed method allows for the simulation of PRD lines in a time series of radiation-magnetohydrodynamic models, in order to interpret observations of chromospheric lines at high spatial resolution.