We report the discovery of a peculiar H I velocity field in the nearby amorphous dwarf starburst galaxy NGC 5253 which indicates that the bulk of the neutral atomic gas rotates about the galaxy’s optical major axis. There is also weak evidence for a second H I dynamical component rotating about the optical minor axis. We estimate the dynamical mass at 3 X 108/sin2 i MQ. The gasdynamics in NGC 5253 are vaguely reminiscent of what is seen in polar ring galaxies and dust lane ellipticals, but the large gas mass fraction (-0.6 for i = 50°), young starburst population, irregular optical morphology, lack of a stellar ring, and lack of stellar rotation (< 7 km s-1) are inconsistent with either type of object. NGC 5253’s unique gasdynamics and current star formation activity may be either (1) the result of an interaction with the nearby spiral M83 -109 yr ago or (2) due to the disruption and accretion of a gas-rich companion on a highly inclined orbit. A combination of wide-field, high-sensitivity H I mapping and new optical spectra measuring the stellar kinematics along the minor axis could discriminate between these two possible interaction scenarios and constrain the original, preinteraction nature of NGC 5253. It is possible that NGC 5253 will later develop into a polar ring galaxy and that we are observing it during its period of ring formation.