An algorithm for identifying rings in Ring Imaging Cherenkov (RICH) detectors is described. The algorithm is necessarily Bayesian and makes use of a Metropolis-Hastings Markov chain Monte Carlo sampler to locate the rings. In particular, the sampler employs a novel proposal function whose form is responsible for significant speed improvements over similar methods. The method is optimised for finding multiple overlapping rings in detectors which can be modelled well by the LHbC RICH toy model described herein.