The Counter Rotating Open Rotor (CROR) powerplant is an interesting architecture for future regional aircraft propulsion since it offers higher propulsive efficiency and thereby lower fuel consumption than the conventional Turbofan engine. The noise levels generated are however potentially larger compared to a Turbofan due in part to the absence of a ducting nacelle. This raises the need for efficient, high fidelity tools that can be used for the design and evaluation of new blade concepts capable of meeting strict noise regulations. In this paper, a Computational Aeroacoustics (CAA) platform for CRORs based on the Harmonic Balance method is presented. The method is formulated in the time domain and solves for the dominant frequencies of the flow by expressing the solution as a truncated Fourier series in time. Coupling between the resolved frequencies is furthermore possible since the nonlinear URANS equations are solved for. The far field acoustic signature is obtained by solving a convective form of the Ffowcs Williams-Hawkings equations for permeable surfaces. The CAA platform is applied to a generic, full scale, pusher type CROR operating at cruise conditions.