  We study compact stars that contain quark matter. We look at the effect of
color superconductivity in the quark matter on the nuclear-quark matter
transition density, mass-radius relationship, and the density discontinuity at
the boundary between nuclear and quark matter. We find that color
superconducting quark matter will occur in compact stars at values of the bag
constant where ordinary quark matter would not be allowed. We are able to
construct ``hybrid'' stars with a color superconducting quark matter interior
and nuclear matter surface, with masses in the range 1.3-1.6 M_solar and radii
8-11 km. Our results are consistent with recent mass-radius limits based on
absorption lines from EXO0748-676.
