Faraday rotation in the VLBI core of BL lacertae

External Faraday rotation has been detected in both the core and the parsec -scale jet of BL Lac in a four-frequency very long baseline interferometry (VLBI) experiment. This unexpected result indicates the presence of signifi cant amounts of thermal gas close to the nucleus of this object. The rotati on measure (RM) in the jet components is constant, and differs from the cur rently accepted Galactic RM, indicating that this value (-205 rad m(-2)) is not applicable to the components in the parsec-scale jet. The similarity o f the RM in these jet components leads us to suspect that the jet RM is cau sed by a foreground screen in our Galaxy, although we cannot rule out a com bination of Galactic RM and RM local to the jet. If the jet RM is due solel y to the Galaxy, this would mean that the currently accepted value of the f oreground RM (-205 rad m(-2)) is not correct, either because the value chan ged between 1982 and 1997, or because the assumption of no intrinsic source rotation was incorrect, as it was at our later epoch of observation. Our o bservations suggest a value of -108 +/- 19 rad m(-2). After correcting for the foreground RM the core value is -427 rad m(-2), wh ich is unexpected since, owing to the weakness of their line emission, BL L ac objects are often assumed to be depleted in gas. The core RM appears to be variable, probably because of the presence of at least two polarized com ponents close to the core the relative contributions of which vary with tim e.