  Let $V$ be a closed 3-manifold with a contact form $\lambda$, and let $L$ be
a link consisting of closed orbits for the Reeb vector field of $\lambda$. We
study the problem of defining cylindrical contact homology on the non-compact
manifold $V \backslash L$, giving sufficient conditions on a class of forms so
that the chain complex can be defined in the expected way. Under further
technical assumptions we show that the homology of the complex up to
isomorphism is independent of choices except possibly the values of certain
Conley-Zehnder indices associated with $L$. A simple example shows that the
homology can depend on the Conley-Zehnder indices of the components of $L$.
