We show preliminary results of an ongoing investigation aimed at determining the configuration of the magnetic field vector in the threads of a quiescent hedgerow solar prominence using high-spatial resolution spectropolarimetric observations taken in the He I 1083.0 nm multiplet. The data consist of a two-dimensional map of a quiescent hedgerow prominence showing vertical threads. The observations were obtained with the Tenerife Infrared Polarimeter attached to the German Vacuum Tower Telescope at the Observatorio del Teide (Spain). The He I 1083.0 nm Stokes signals are interpreted with an inversion code, which takes into account the key physical processes that generate and/or modify circular and linear polarization signals in the He I 1083.0 nm triplet: the Zeeman effect, anisotropic radiation pumping, and the Hanle effect. We present initial results of the inversions, i.e, the strength and orientation of the magnetic field vector along the prominence and in prominence threads.