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We evaluated the 3D spatial, energy, and timing resolution of the Brain (or Breast)-Initiative Next-Generation (BING) PET detector. The BING detector is an array of 1-mm-thick slats of LYSO scintillator with lapped specular-reflective faces (15-mm by 52-mm) that are stacked together and oriented with their long-narrow edges normal to the imaging field of view. Interaction positions are determined from the signals of silicon-photomultiplier (SiPM) arrays placed on the entrance (top) and exit (bottom) faces. The SiPM arrays are offset to determine the slat of interaction (SOI) without requiring any optical light sharing between slats. Maximum likelihood 2D location within the SOI is determined using the sensor signals. Interaction time is determined with a modified first-optical-photon pickoff method. Performance of the BING detector was measured as a function of position using a sideways coincidence-collimated beam. Slats were accurately identified, with an effective tangential detector resolution of 1 mm. Average resolutions (and ranges) are: 0.96 mm (0.85 mm to 1.11 mm) for lateral (axial) detector resolution, 1.6 mm (1.0 mm to 2.1 mm) for depth resolution, 13.6% (12.7% to 16.0%) for energy resolution, and 317 ps (241 ps to 404 ps) for coincidence timing resolution. Initial spatial and timing resolution results demonstrated that the BING detector can be effective in a small field-of view (e.g., brain or breast) PET system.