Urban Air Mobility (UAM) vehicles are intended to operate near or within large cities, where a significant portion of the public will be exposed to the noise they create. If these vehicles are to become acceptable to the public, designers must be able to manage the amount of noise they generate, and understand the relationship between traditional performance metrics (thrust, efficiency, etc.) and noise. As a first step to addressing this need, this work combines a Blade Element Momentum Theory tool (OpenBEMT) with an acoustic prediction tool (ANOPP2) to optimize a propeller subject to both aerodynamic and acoustic constraints. These tools are developed within a optimization framework (OpenMDAO (Multidisciplinary Design Analysis Optimization)) that allows analytic derivatives to be propagated through the models and passed to a gradient-based optimizer. This tool chain is exercised on the cruise propellers from the X-57 Maxwell, and yields propeller designs that reduced the overall sound pressure level by about 8 decibels for a cost of 3 percent propeller efficiency.