  The Chaplygin gas has been proposed as a possible dark energy, dark matter
candidate. As a working fluid in a Friedmann-Robertson-Walker universe, it
exhibits early behavior reminiscent of dark matter, but at later times is more
akin to a cosmological constant. In any such universe, however, one can expect
local perturbations to form. Here we obtain the general equations for a
self-gravitating relativistic Chaplygin gas. We solve these equations and
obtain the mass-radius relationship for such structures, showing that only in
the phantom regime is the mass-radius relationship large enough to be a serious
candidate for highly compact massive objects at the galaxy core. In addition,
we study the cosmology of a modified anti-Chaplygin gas. A self-gravitating
cloud of this matter is an exact solution to Einstein's equations.
