Long-period comet C/2014 B1 (Schwartz) exhibits a remarkable optical appearance, like that of a discus or bi-convex lens viewed edgewise. Our measurements in the four years since discovery reveal a unique elongated dust coma whose orientation is stable with respect to the projected antisolar and orbital directions. With no tail and no trail, the limited influence of radiation pressure on the dust coma sets a lower limit to the effective particle size ≳100 μm, while the photometry reveals a peak coma scattering cross-section 2.7 × 104 km2 (geometric albedo 0.1 assumed). From the rate of brightening of the comet we infer a dust production rate ≳10 kg s-1 at 10 au heliocentric distance, presumably due to the sublimation of supervolatile ices, and perhaps triggered by the crystallization of amorphous water ice. We consider several models for the origin of the peculiar morphology. The disk-like shape is best explained by equatorial ejection of particles from a nucleus whose spin vector lies near the plane of the sky. In this interpretation, the unique appearance of C/2014 B1 is a result of a near equality between the rotation-assisted nucleus escape speed (̃1-10 m s-1 for a 2-20 km scale nucleus) and the particle ejection velocity, combined with a near-equatorial viewing perspective. To date, most other comets have been studied at heliocentric distances less than half that of C/2014 B1, where their nucleus temperatures, gas fluxes, and dust ejection speeds are much higher. The throttling role of nucleus gravity is correspondingly diminished, so that the disk morphology has not before been observed.