  A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces
a linearization of the contact homology of $M$ with corresponding linearized
contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the
symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to
$HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we
give a description of the degree -2 map in terms of rational holomorphic curves
with constrained asymptotic markers, in the symplectization of $M$.
