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

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... . 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^+0.12x 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]