  Dense matter in compact stars cools efficiently by neutrino emission via the
direct Urca processes n -> p + e + nu and p + e -> n + nu. Below the pairing
phase transition temperature Tc these processes are suppressed - at
asymptotically low temperatures exponentially. We compute the emissivity of the
Urca process at one loop for temperatures T < Tc, in the case where the baryons
are paired in the 1S0 partial wave. The Urca process is suppressed linearly,
rather than exponentially, within the temperature range 0.1 < T/Tc < 1. The
charge-current Cooper pair-breaking process contributes up to 50% of the total
Urca emissivity in this temperature range.
