Substantial populations of massive quiescent galaxies at z ≥ 3 challenge our understanding of rapid galaxy growth and quenching over short timescales. In order to piece together this evolutionary puzzle, more statistical samples of these objects are required. Established techniques for identifying massive quiescent galaxies are increasingly inefficient and unconstrained at z > 3. As a result, studies report that as much as 70% of quiescent galaxies at z > 3 may be missed from existing surveys. In this work, we propose a new empirical color selection technique designed to select massive quiescent galaxies at 3 ≲ z ≲ 6 using JWST NIRCam imaging data. We use empirically constrained galaxy spectral energy distribution (SED) templates to define a region in the F277W − F444W versus F150W − F277W color plane that captures quiescent galaxies at z > 3. We apply these color selection criteria to the Cosmic Evolution Early Release Science (CEERS) Survey and use SED fitting on sources in the region to identify 44 candidate z ≳ 3 quiescent galaxies. Over half of these sources are newly discovered and, on average, exhibit specific star formation rates of poststarburst galaxies. Most of these sources would not be discovered using canonical UVJ diagrams. We derive volume density estimates of n ∼ 1-4 × 10−5 Mpc−3 at 3 < z < 5, finding excellent agreement with existing reports on similar populations in the CEERS field. Thanks to NIRCam’s wavelength coverage and sensitivity, this technique provides an efficient tool to search for large samples of these rare galaxies.