The disclosed invention is embodied in an improved LED-based lighting fixture for projecting a beam of light having a substantially uniform intensity, rotationally, and a selectable, substantially uniform chromaticity. The lighting fixture includes (1) a concave reflector having circumferential facets, a focal region, an aperture, and a central opening; and (2) a light source assembly including two or more groups of LEDs mounted at the forward end of an elongated, thermally conductive support. The light source assembly is mounted relative to the reflector with the elongated support's longitudinal axis aligned with the reflector's longitudinal axis and with the groups of LEDs located at or near the reflector's focal region. Each of the two or more groups of LEDs includes a plurality of LEDs arranged in a specific pattern such that they cooperate with the faceted concave reflector to project a beam of light having a selectable, substantially uniform chromaticity.