We have detected likely z~7-8 galaxies in the144''×144'' Near-Infrared Camera andMulti-Object Spectrometer (NICMOS) observations of the Hubble Ultra DeepField. Objects are required to be >=3 σ detections in bothNICMOS bands, J110 and H160. The selectioncriteria for this sample are(z850-J110)AB>0.8,(z850-J110)AB>0.66(J110-H160)AB+0.8,(J110-H160)AB<1.2 and no detectionat less than 8500 Å. The five selected sources have totalmagnitudes H160,AB~27. Four of the five sources are quiteblue compared to typical lower redshift dropout galaxies and areclustered within a 1 arcmin2 region. Because all five sourcesare near the limit of the NICMOS data, we have carefully evaluated theirreality. Each of the candidates is visible in different splits of thedata and a median stack. We analyzed several noise images and estimatethe number of spurious sources to be 1+/-1. A search using anindependent reduction of this same data set clearly revealed three ofthe five candidates and weakly detected a fourth candidate, suggestingthat the contamination could be higher. For comparison with predictionsfrom lower redshift samples, we take a conservative approach and adoptfour z~7-8 galaxies as our sample. With the same detection criteria onsimulated data sets, assuming no evolution from z~3.8, we predict 10sources at z~7-8, or 14 if we use a more realistic (1+z)-1size scaling. We estimate that the rest-frame continuum UV (~1800Å) luminosity density at z~7.5 (integrated down to0.3L*z=3) is just0.20+0.12-0.08 times that found at z~3.8 (or0.20+0.23-0.12 times this quantity includingcosmic variance). Effectively this sets an upper limit on the luminositydensity down to 0.3L*z=3 and is consistent withsignificant evolution at the bright end of the luminosity function fromz~7.5 to 3.8. Even with the lower UV luminosity density at z~7.5, itappears that galaxies could still play an important role in reionizationat these redshifts, although definitive measurements remain to be made.Based on observations made with the NASA/ESA Hubble Space Telescope,which is operated by the Association of Universities for Research inAstronomy, Inc., under NASA contract NAS 5-26555.