Photon scattering in the extended wings of many strong resonance lines is nearly coherent under typical stellar chromospheric conditions, with free-electron densities of about 10(12) cm-3 or less. When photon transport in these partially coherent wings dominates escape from the chromosphere, the depth of line thermalization will be strongly affected. Such effects of partial redistribution (PRD) are not accounted for in standard two-level thermalization models involving complete redistribution (CRD). We investigate the conditions necessary for partially coherent scattering to influence the thermalization depth, and approximate these effects in homogeneous slab atmospheres, using several common resonance lines as examples. For electron densities above 10(10) cm-3, we conclude that even when coherent scattering dominates the escape process, the thermalization depths of the strongest resonance lines of H, Ca II, and Mg II agree roughly with the standard result for complete redistribution over a Doppler profile. This occurs because of the importance of Doppler diffusion in frequency. However, at lower densities, such as for giant star chromospheres and QSO models, the results deviate strongly from the Doppler CRD case.