  We implement relativistic BCS superconductivity in N=1 supersymmetric field
theories with a U(1)_R symmetry. The simplest model contains two chiral
superfields with a Kahler potential modified by quartic terms. We study the
phase diagram of the gap as a function of the temperature and the specific
heat. The superconducting phase transition turns out to be first order, due to
the scalar contribution to the one-loop potential. By virtue of supersymmetry,
the critical curves depend logarithmically with the UV cutoff, rather than
quadratically as in standard BCS theory. We comment on the difficulties in
having fermion condensates when the chemical potential is instead coupled to a
baryonic U(1)_B current. We also discuss supersymmetric models of BCS with
canonical Kahler potential constructed by "integrating-in" chiral superfields.
