Fibrils are thin elongated features visible in the solar chromosphere in and around magnetized regions. Because of their visual appearance, they have been traditionally considered a tracer of the magnetic field lines. For the first time, we challenge that notion by comparing their orientation to that of the magnetic field, obtained via high-resolution spectorpolarimetric observations of CaII lines. The short answer to the question posed in the title is that mostly yes, but not always.