We present an examination of high-resolution, ultraviolet (UV) spectroscopy from Hubble Space Telescope of the photospheric spectrum of the O-supergiant in the massive X-ray binary HD 226868 = Cyg X-1. We analyzed this and ground-based optical spectra to determine the effective temperature and gravity of the O9.7 Iab supergiant. Using non-LTE, line-blanketed, plane-parallel models from the TLUSTY grid, we obtain T eff = 28.0 ± 2.5 kK and log g gsim 3.00 ± 0.25, both lower than in previous studies. The optical spectrum is best fit with models that have enriched He and N abundances. We fit the model spectral energy distribution for this temperature and gravity to the UV, optical, and infrared (IR) fluxes to determine the angular size and extinction toward the binary. The angular size then yields relations for the stellar radius and luminosity as a function of distance. By assuming that the supergiant rotates synchronously with the orbit, we can use the radius-distance relation to find mass estimates for both the supergiant and black hole (BH) as a function of the distance and the ratio of stellar to Roche radius. Fits of the orbital light curve yield an additional constraint that limits the solutions in the mass plane. Our results indicate masses of 23+8 -6 M sun for the supergiant and 11+5 -3 M sun for the BH. Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. These observations are associated with programs GO-9646 and GO-9840.