  We construct a one-parameter family of five-dimensional N=2 supergravity
Lagrangians with an SU(2,1) / U(2) hypermultiplet. For certain values of the
parameter, these are argued to describe the dynamics of scalar modes of
superstrings on AdS_5 x T^{1,1}, and therefore to be dual to specific chiral
primary operators of Klebanov-Witten superconformal field theory. We
demonstrate that, below a critical temperature, the thermodynamics is dominated
by charged black holes with hair for the scalars that are dual to the operator
of lowest conformal dimension 3/2. The system thus enters into a
superconducting phase where <Tr[A_k B_l]> condenses.
