  We have detected likely z~7-8 galaxies in the 144"x144" NICMOS observations
of the Hubble Ultra Deep Field. Objects are required to be >3 sigma detections
in both NICMOS bands, J and H. The selection criteria for this sample are
(z-J)>0.8, (z-J) > 0.66 (J-H)+0.8, (J-H)<1.2, and no detection at <8500
Angstroms. The 5 selected sources have total magnitudes H~27. Four of the five
sources are quite blue compared to typical lower-redshift dropout galaxies and
are clustered within a 1 arcmin**2 region. Because all 5 sources are near the
limit of the NICMOS data, we have carefully evaluated their reality. Each of
the candidates is visible in different splits of the data and a median stack.
We analyzed several noise images and estimate the number of spurious sources to
be 1+/-1. A search using an independent reduction of this same data set clearly
revealed 3 of the 5 candidates and weakly detected a 4th candidate, suggesting
the contamination could be higher. For comparison with predictions from lower
redshift samples we take a conservative approach and adopt four z~7-8 galaxies
as our sample. With the same detection criteria on simulated datasets, assuming
no-evolution from z~3.8, we predict 10 sources at z~7-8, or 14 if we use a more
realistic (1+z)^{-1} size scaling. We estimate that the rest-frame continuum UV
(~1800 Angstroms) luminosity density at z~7.5 (integrated down to 0.3L*) is
just 0.20_{-0.08}^{+0.12}x that found at z~3.8. Effectively this sets an upper
limit on the luminosity density down to 0.3 L*. This result is consistent with
significant evolution at the bright end of the luminosity function from z~7.5
to z~3.8. Even with the lower UV luminosity density at z~7.5, it appears that
galaxies could still play an important role in reionization at these redshifts,
though definitive measurements remain to be made. [abridged]
