Full-Stokes spectropolarimetric data (in the 10830 Å region) of an active region filament were obtained in July 2005 using the Tenerife Infrared Polarimeter instrument. The polarization profiles in the filament show Zeeman-like signatures. Milne-Eddington inversions were performed to infer the chromospheric magnetic field, inclination, azimuth, velocity and Doppler width from the He I 10830 Å multiplet. Field strengths of the order of 600-800 G were found in the filament. Strong transverse fields at chromospheric levels were detected near the polarity inversion line. To our knowledge, these are the highest field strengths reliably measured in these structures. Our findings suggest the possible presence of a flux rope.