Abstract. Hyperbolic surfaces of finite volume are objects of study in Quantum Chaos since the geodesic flow on such surfaces is known to be ergodic. Selberg's trace formula famously links the eigenvalues of the Laplacian on such a surface to geometric quantities such as periodic orbits. I will present an analogue of Selberg's trace formula for a delta potential on a hyperbolic surface. In the case of a non-compact surface with a single cusp I will present perturbative analogues of classical Maass forms and nonholomorphic Eisenstein series which naturally arise in the development of the trace formula.