We report Doppler-only (cw) radar observations of basaltic near-Earth asteroid 3908 Nyx obtained at Arecibo and Goldstone in September and October of 1988. The circular polarization ratio of 0.75±0.03 exceeds ̃90% of those reported among radar-detected near-Earth asteroids and it implies an extremely rough near-surface at centimeter-to-decimeter spatial scales. Echo power spectra over narrow longitudinal intervals show a central dip indicative of at least one significant concavity. Inversion of cw spectra yields two statistically indistinguishable shape models that have similar shapes and dimensions but pole directions that differ by ̃100°. We adopt one as our working model and explore its implications. It has an effective diameter of 1.0±0.15 km and radar and visual geometric albedos of 0.15±0.075 and 0.16 +0.08-0.05. The visual albedo supports the interpretation by D. P. Cruikshank et al. (1991, Icarus89, 1-13) that Nyx has a thermal inertia consistent with that of bare rock. The model is irregular, modestly asymmetric, and topographically rugged.