  The three-flavor crystalline color-superconducting (CCS) phase of quantum
chromodynamics (QCD) is a candidate phase for the ground state of cold matter
at moderate densities above the density of the deconfinement phase transition.
Apart from being a superfluid, the CCS phase has properties of a solid, such as
a lattice structure and a shear modulus, and hence the ability to sustain
multipolar deformations in gravitational equilibrium. We construct equilibrium
configurations of hybrid stars composed of nuclear matter at low, and CCS quark
matter at high, densities. Phase equilibrium between these phases is possible
only for rather stiff equations of state of nuclear matter and large couplings
in the effective Nambu--Jona-Lasinio Lagrangian describing the CCS state. We
identify a new branch of stable CCS hybrid stars within a broad range of
central densities which, depending on the details of the equations of state,
either bifurcate from the nuclear sequence of stars when the central density
exceeds that of the deconfinement phase transition or form a new family of
configurations separated from the purely nuclear sequence by an instability
region. The maximum masses of our non-rotating hybrid configurations are
consistent with the presently available astronomical bounds. The sequences of
hybrid configurations that rotate near the mass-shedding limit are found to be
more compact and thus support substantially larger spins than their same mass
nuclear counterparts.
