We present a hybrid approach to groundwater transport modeling, “CTRW-on-a-streamline,” that allows continuous-time random walk (CTRW) particle tracking on large-scale, explicitly delineated heterogeneous groundwater velocity fields. The combination of a non-Fickian transport model (in this case, the CTRW) with general heterogeneous velocity fields represents an advance of the current state of the art, in which non-Fickian transport models or heterogeneous velocity fields are employed but generally not both. We present a general method for doing this particle tracking that fully separates the model parameters characterizing macroscopic flow, subscale advective heterogeneity, and mobile-immobile mass transfer, such that each can be directly specified a priori from available data. The method is formalized and connections to classic CTRW and subordination approaches are made. Numerical corroboration is presented.