We develop a genetic algorithm that produces neural network feedback controllers for chaotic systems. The algorithm was tested on the logistic and Henon maps, for which it stabilizes an unstable fixed point using small perturbations, even in the presense of significant noise. The network training method [D. E. Moriarty and R. Miikkulainen, Mach. Learn. 22, 11 (1996)] requires no previous knowledge about the system to be controlled, including the dimensionality of the system and the location of unstable fixed points. This is the first dimension-independent algorithm that produces neural network controllers using time-series data. A software implementation of this algorithm is available here.