A model of cosmological inflation is proposed in which field space is a hyperbolic plane. The inflaton never slow-rolls, and instead orbits the bottom of the potential, buoyed by a centrifugal force. Though initial velocities redshift away during inflation, in negatively curved spaces angular momentum naturally starts exponentially large and remains relevant throughout. Quantum fluctuations produce perturbations that are adiabatic and approximately scale invariant; strikingly, in a certain parameter regime the perturbations can grow double exponentially during horizon crossing.