We measured infrared surface brightness fluctuation (SBF) distances to an isotropically-distributed sample of 16 distant galaxies with redshifts reaching 10,000 km/s using the near-IR camera and multi-object spectrometer (NICMOS) on the Hubble Space Telescope (HST). The excellent spatial resolution, very low background, and brightness of the IR fluctuations yielded the most distant SBF measurements to date. Twelve nearby galaxies were also observed and used to calibrate the F160W (1.6 micron) SBF distance scale. Of these, three have Cepheid variable star distances measured with HST and eleven have optical I-band SBF distance measurements. A distance modulus of 18.5 mag to the Large Magellanic Cloud was adopted for this calibration. We present the F160W SBF Hubble diagram and find a Hubble constant Ho=76 +/- 1.3 (1-sigma statistical) +/- 6 (systematic) km/s/Mpc. This result is insensitive to the velocity model used to correct for local bulk motions. Restricting the fit to the six most distant galaxies yields the smallest value of Ho=72 +/- 2.3 km/s/Mpc consistent with the data. This 6% decrease in the Hubble constant is consistent with the hypothesis that the Local Group inhabits an under-dense region of the universe, but is also consistent with the best-fit value of Ho=76 km/s/Mpc at the 1.5-sigma level.

39 pages, 7 figures, accepted for publication in ApJ