A rotational modulator (RM) gamma-ray imager is capable of obtaining significantly better angular resolution than the fundamental geometric resolution defined by the ratio of detector diameter to mask-detector separation. An RM imager consisting of a single grid of absorbing slats rotating ahead of an array of a small number of position-insensitive detectors has the advantage of fewer detector elements (i.e., detector plane pixels) than required by a coded aperture imaging system with comparable angular resolution. The RM therefore offers the possibility of a major reduction in instrument complexity, cost, and power. A novel image reconstruction technique makes it possible to deconvolve the raw images, remove sidelobes, reduce the effects of noise, and provide resolving power a factor of 6 -8 times better than the geometric resolution. A 19-channel prototype RM developed in our laboratory at Louisiana State University features 13.8• full-angle field of view, 1.9• geometric angular resolution, and the capability of resolving sources to within 35 ′ separation. We describe the technique, demonstrate the measured performance of the prototype instrument, and describe the prospects for applying the technique to either a high-sensitivity standoff gamma-ray imaging detector or a satelliteor balloon-borne gamma-ray astronomy telescope.