We used HST to obtain surface brightness fluctuation (SBF) observations of four nearby brightest cluster galaxies (BCG) to calibrate the BCG Hubble diagram of Lauer & Postman (1992). This BCG Hubble diagram contains 114 galaxies covering the full celestial sphere and is volume limited to 15,000 km/s, providing excellent sampling of the far field Hubble flow. The SBF zero point is based on the Cepheid calibration of the ground I_KC method (Tonry et al. 1997) as extended to the WFPC2 F814W filter by Ajhar et al. (1997). The BCG globular cluster luminosity functions give distances essentially identical to the SBF results. Using the velocities and SBF distances of the four BCG alone gives H_0 = 82 +/- 8 km/s/Mpc in the CMB frame, valid on ~4,500 km/s scales. Use of BCG as photometric redshift estimators allows the BCG Hubble diagram to be calibrated independently of recession velocities, yielding a far field H_0 = 89 +/- 10 km/s/Mpc with an effective depth of ~11,000 km/s. The error in this case is dominated by the photometric cosmic scatter in using BCG as distance estimators. The concordance of the present results with other recent H_0 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 H_0 depend more on understanding nearby calibrators than on improved sampling of the distant flow.

18 pages; figure[1-2,7-9].ps are EPS files included in body of text, figure[3-6].jpg are JPEG images not included; LaTeX (AASTeX v4.0); Submitted to The Astrophysical Journal. Compressed PostScript of entire paper with all figures included is available at ftp://mars.tuc.noao.edu/sbf/hubble.ps.gz