We report photometric observations of the eclipsing close binary CSS21055 (SDSS J141126+200911) that strongly suggest that the companion to the carbon-oxygen white dwarf is a brown dwarf with a mass between 0.030 and 0.074M_{sun}. The measured orbital period is 121.73-min and the totality of the eclipse lasts 125s. If confirmed, CSS21055 would be the first detached eclipsing WD+BD binary. Spectroscopy in the eclipse could provide information about the companion's evolutionary state and atmospheric structure.