We report the discovery of a medium-strength (∼0.5 kG) magnetic field on the young, massive star τ Sco (B0.2 V), which becomes the third-hottest magnetic star known. Circularly polarized Zeeman signatures are clearly detected in observations collected mostly with the ESPaDOnS spectropolarimeter, recently installed on the 3.6-m Canada-France-Hawaii Telescope; temporal variability is also clearly established in the polarimetry, and can be unambiguously attributed to rotational modulation with a period close to 41 d. Archival ultraviolet (UV) spectra confirm that this modulation repeats over time-scales of decades, and refine the rotation period to 41.033 ± 0.002 d.Despite the slow rotation rate of τ Sco, we none the less succeed in reconstructing the large-scale structure of its magnetic topology. We find that the magnetic structure is unusually complex for a hot star, with significant power in spherical-harmonic modes of degree up to 5. The surface topology is dominated by a potential field, although a moderate toroidal component is probably present. We fail to detect intrinsic temporal variability of the magnetic structure over the 1.5-yr period of our spectropolarimetric observations (in agreement with the stable temporal variations of the UV spectra), and infer that any differential surface rotation must be very small.The topology of the extended magnetic field that we derive from the photospheric magnetic maps is also more complex than a global dipole, and features in particular a significantly warped torus of closed magnetic loops encircling the star (tilted at about 90 • to the rotation axis), with additional, smaller, networks of closed-field lines. This topology appears to be consistent with the exceptional X-ray properties of τ Sco and also provides a natural explanation of the variability observed in wind-formed UV lines. Although we cannot completely rule out the possibility that the field is produced through dynamo processes of an exotic kind, we conclude that its magnetic field is most probably a fossil remnant from the star formation stage.Based on observations obtained at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National