  We study QCD with one flavor at finite baryon density. In the limit of very
high baryon density the system is expected to be a color superconductor. In the
case of one flavor, the order parameter is in a $\bar 3$ of color and has total
angular momentum one. We show that in weak coupling perturbation theory, the
energetically preferred phase exhibits ``color-spin-locking'', i.e. the color
and spin direction of the condensate are aligned. We discuss the properties of
this phase and argue that it shares important features of the hadronic phase at
low density. In particular, we find an unbroken rotational symmetry, spin 3/2
quasiparticles, and an unusual mechanism for quark-anti-quark condensation. Our
results are relevant to three flavor QCD in the regime where the strange quark
mass is bigger than the critical value for color-flavor-locking. We find that
the gaps in this case are on the order of one MeV.
