We study resonance curves of nonlinear dynamical systems with chaotic forcing functions. We use the calculus of variations to determine the forcing function that induces the largest response. We compute the resonant forcing for a set of model systems and determine the response of the dynamical system to each forcing function. We show that the response is largest if the model system matches the dynamical system. We find that the signal to noise ratio is particularly large if one of the Lyapunov exponents is large.