We used the Hubble Space Telescope to obtain surface brightness fluctuation (SBF) observations of four nearby brightest cluster galaxies (BCGs) to calibrate the BCG Hubble diagram of Lauer & Postman. This BCG Hubble diagram contains 114 galaxies covering the full celestial sphere and is volume-limited to 15,000 km s-1, providing excellent sampling of the far-field Hubble flow. The SBF zero point is based on the Cepheid calibration of the ground IKC method as extended to the WFPC2 F814W filter by Ajhar and coworkers. The BCG globular cluster luminosity functions give distances essentially identical to the SBF results. Using the velocities and SBF distances of the four BCGs alone gives H0 = 82 +/- 8 km s-1 Mpc-1 in the CMB frame, valid on ~4500 km s-1 scales; the error includes both systematic and random contributions. Use of BCGs as photometric redshift estimators allows the BCG Hubble diagram to be calibrated independently of recession velocities of the four nearby BCGs, yielding a far-field H0 = 89 +/- 10 km s-1 Mpc-1 with an effective depth of ~11,000 km s-1. The larger error in this case is due to the photometric cosmic scatter in using BCGs as redshift estimators; this H0 is not significantly different from the more local value. The concordance of the present results with other recent H0 determinations and a review of theoretical treatments on perturbations in the near-field Hubble flow argue that going to the far field removes an important source of uncertainty, but that there is not a large systematic error to be corrected for to begin with. Further improvements in H0 depend more on understanding nearby calibrators than on improved sampling of the distant flow.Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under NASA contract NAS 5-26555.