  We calculate the sutured version of cylindrical contact homology of a sutured
contact solid torus $(S^1\times D^2,\Gamma, \xi)$, where $\Gamma$ consists of
$2n$ parallel sutures of arbitrary slope and $\xi$ is a universally tight
contact structure. In particular, we show that it is non-zero. This computation
is one of the first computations of the sutured version of cylindrical contact
homology and does not follow from computations in the closed case.
