Tetrahedrally bonded amorphous carbon (ta-C) is a predominately sp3-bonded semiconductor with a band gap of order 2 eV. It can be doped n-type using nitrogen but no successful p-type doping has been reported until now. On the other hand, it has recently been shown that the incorporation of boron reduces the intrinsic compressive stress of ta-C, while still maintaining its high fraction of sp3 sites. This paper reports a detailed study of the electrical properties of boron-doped ta-C (ta-C:B). The ta-C:B films are deposited in a filtered cathodic vacuum arc system using a pressed cathode of graphite and boron powder. The composition and structure of the films are examined by electron energy loss spectroscopy. We find that the room temperature conductivity of the films increases by five orders of magnitude with a boron concentration from 0 to 8%. The conductivity activation energy decreases for the same boron concentration, while the E04 gap remains constant. N-type silicon/ta-C:B heterojunctions show a rectifying behaviour as a function of the boron concentration of the films. The films show photo-conductivity. The combined results indicate p-type doping of ta-C.