Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics (A. Bouillantet al.,Nature Physics,141188–1192, 2018). Motivated by these experiments, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small in comparison to the capillary length.The model couples the equations of motion of the drop, which flows as a rigid wheel, and a thin-film model governing the vapor flow, the profile of the deformable vapor-liquid interface and thus the hydrodynamic forces and torques on the drop. In contrast to previous analytical models of Leidenfrost drops, which predict only symmetric solutions, we find that the symmetric Leidenfrost state is unstable above a critical drop radius: R1 for a free drop and R2> R1 for an immobilized drop. In these respective cases, symmetry breaking is manifested in supercritical-pitchfork bifurcations into steady states of pure rolling and constant angular velocity. In further qualitative agreement with the experiments, when a symmetry-broken immobilized drop is suddenly released it initially moves at constant accelerationαg, whereαis an angle characterizing the slope of the liquid-vapor profile and g is the gravitational acceleration; moreover,αexhibits a maximum with respect to the drop radius, at a radius increasing with the temperature difference between the surface and the drop.