It is argued that the superfluid core of a neutron star super-rotates relative to the crust, because stratification prevents the core from responding to the electromagnetic braking torque, until the relevant dissipative (viscous or Eddington-Sweet) time-scale, which can exceed ∼ 10 3 yr and is much longer than the Ekman timescale, has elapsed. Hence, in some young pulsars, the rotation of the core today is a fossil record of its rotation at birth, provided that magnetic crust-core coupling is inhibited, e.g. by buoyancy, field-line topology, or the presence of uncondensed neutral components in the superfluid. Persistent core super-rotation alters our picture of neutron stars in several ways, allowing for magnetic field generation by ongoing dynamo action and enhanced gravitational wave emission from hydrodynamic instabilites.1 In this paper, we restrict attention to the spin-down problem relevant to an electromagnetically braking neutron star.