This paper investigates the performance of 1 mm resolution Cadmium Zinc Telluride (CZT) detectors for positron emission tomography (PET) capable of positioning the 3-D coordinates of individual 511 keV photon interactions. The detectors comprise 40 mm × 40 mm × 5 mm monolithic CZT crystals that employ a novel cross-strip readout with interspersed steering electrodes to obtain high spatial and energy resolution. The study found a single anode FWHM energy resolution of 3.06±0.39% at 511 keV throughout most the detector volume. Improved resolution is expected with properly shielded front-end electronics. Measurements made using a collimated beam established the efficacy of the steering electrodes in facilitating enhanced charge collection across anodes, as well as a spatial resolution of 0.44±0.07 mm in the direction orthogonal to the electrode planes. Finally, measurements based on coincidence electronic collimation yielded a point spread function with 0.78±0.10 mm FWHM, demonstrating 1 mm spatial resolution capability transverse to the anodes – as expected from the 1 mm anode pitch. These findings indicate that the CZT-based detector concept has excellent performance and shows great promise for a high-resolution PET system.