We present VLT/FORS2 time-series spectroscopy of the Wolf-Rayet star # 41 in the Sculptor group galaxy NGC 300 . We confirm a physical association with NGC 300 X–1 , since radial velocity variations of the He ii \lambda 4686 line indicate an orbital period of 32.3 \pm 0.2 hr which agrees at the 2 \sigma level with the X-ray period from Carpano et al . We measure a radial velocity semi-amplitude of 267 \pm 8 km s ^ { -1 } , from which a mass function of 2.6 \pm 0.3 M _ { \odot } is obtained . A revised spectroscopic mass for the WN-type companion of 26 ^ { +7 } _ { -5 } M _ { \odot } yields a black hole mass of 20 \pm 4 M _ { \odot } for a preferred inclination of 60 - 75 ^ { \circ } . If the WR star provides half of the measured visual continuum flux , a reduced WR ( black hole ) mass of 15 ^ { +4 } _ { -2.5 } M _ { \odot } ( 14.5 ^ { +3 } _ { -2.5 } M _ { \odot } ) would be inferred . As such , # 41/NGC 300 X–1 represents only the second extragalactic Wolf-Rayet plus black-hole binary system , after IC 10 X–1 . In addition , the compact object responsible for NGC 300 X–1 is the second highest stellar-mass black hole known to date , exceeded only by IC 10 X–1 .