Abstract. The link of the A n singularity, L An ⊂ C 3 admits a natural contact structure ξ 0 coming from the set of complex tangencies. The canonical contact form α 0 associated to ξ 0 is degenerate and thus has no isolated Reeb orbits. We show that there is a nondegenerate contact form for a contact structure equivalent to ξ 0 that has two isolated simple periodic Reeb orbits. We compute the Conley-Zehnder index of these simple orbits and their iterates. From these calculations we compute the positive S 1 -equivariant symplectic homology groups for (L An , ξ 0 ). In addition, we prove that (L An , ξ 0 ) is contactomorphic to the Lens space L(n + 1, n), equipped with its canonical contact structure ξ std .