We propose a Bayesian edge detector to be fed by polarimetric, possibly multifrequency, SAR data. It can be used to detect dark spots on the ocean surface and, hence, as the first stage of a system for identification and monitoring of oil spills. The proposed detector does not require secondary data (namely pixels from a slick-free area), but for a certain a priori knowledge about the spectral properties of the data. The performance assessment, carried out using both synthetic and real SAR recordings, shows that it has better capabilities in terms of detection and false alarms control than previously-proposed classical (i.e., non-Bayesian) detectors.