IC 10 X-1 is a variable X-ray source in the Local Group starburst galaxy IC 10 whose optical counterpart is a Wolf-Rayet (WR) star. Prestwich et al. (2007) recently proposed that it contains the most massive known stellar-mass black hole (23-34 M_sun), but their conclusion was based on radial velocities derived from only a few optical spectra, the most important of which was seriously affected by a CCD defect. Here we present new spectra of the WR star, spanning one month, obtained with the Keck-I 10 m telescope. The spectra show a periodic shift in the He II 4686 Ang. emission line as compared with IC 10 nebular lines such as [O III] 5007 Ang. From this, we calculate a period of 34.93+/-0.04 hr (consistent with the X-ray period of 34.40+/-0.83 hr reported by Prestwich et al. 2007) and a radial-velocity semi-amplitude of 370+/-20 km/s. The resulting mass function is 7.64+/-1.26 M_sun, consistent with that of Prestwich et al. (2007) (7.8 M_sun). This, combined with the previously estimated (from spectra) mass of 35 M_sun for the WR star, yields a minimum primary mass of 32.7+/-2.6 M_sun. Even if the WR star has a mass of only 17 M_sun, the minimum primary mass is 23.1+/-2.1 M_sun. Thus, IC 10 X-1 is indeed a WR/black-hole binary containing the most massive known stellar-mass black hole.
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