Legendrian Contact Homology is a Floer-type invariant of Legendrian submanifolds that (usually) takes the form of a differential graded algebra (DGA) whose homology is invariant under Legendrian isotopy. While it is difficult to extract useful information from the full DGA, a linearized version has proven computable and useful. Over the past decade, ever more algebraic structure of the linearized DGA has been revealed: an Alexander- like duality, cup products, higher Massey products, etc. The goal of this talk will be to review past results from an A-infinity perspective and to show that the cup product structure yields something (pretty close to) a Frobenius algebra. I hope to finish by presenting some evidence that the Frobenius structure generalizes to a cyclic A-infinity algebra.