Recent studies have shown that systems combining mathematical modeling and Bayesian inference methods can be used to generate real-time forecasts of future infectious disease incidence. Here we develop such a system to study and forecast respiratory syncytial virus (RSV). RSV is the most common cause of acute lower respiratory infection and bronchiolitis. Advanced warning of the epidemic timing and volume of RSV patient surges has the potential to reduce well-documented delays of treatment in emergency departments. We use a susceptible-infectious-recovered (SIR) model in conjunction with an ensemble adjustment Kalman filter (EAKF) and ten years of regional U.S. specimen data provided by the Centers for Disease Control and Prevention. The data and EAKF are used to optimize the SIR model and i) estimate critical epidemiological parameters over the course of each outbreak and ii) generate retrospective forecasts. The basic reproductive number, R0, is estimated at 3.0 (standard deviation 0.6) across all seasons and locations. The peak magnitude of RSV outbreaks is forecast with nearly 70% accuracy (i.e. nearly 70% of forecasts within 25% of the actual peak), four weeks before the predicted peak. This work represents a first step in the development of a real-time RSV prediction system.