We have detected likely z \sim 7 - 8 galaxies in the 144 ^ { \prime \prime } \times 144 ^ { \prime \prime } NICMOS observations of the Hubble Ultra Deep Field . Objects are required to be \geq 3 \sigma detections in both NICMOS bands , J _ { 110 } and H _ { 160 } . The selection criteria for this sample are ( z _ { 850 } - J _ { 110 } ) _ { AB } > 0.8 , ( z _ { 850 } - J _ { 110 } ) _ { AB } > 0.66 ( J _ { 110 } - H _ { 160 } ) _ { AB } +0.8 , ( J _ { 110 } - H _ { 160 } ) _ { AB } < 1.2 , and no detection at < 8500 \AA . The 5 selected sources have total magnitudes H _ { 160 ,AB } \sim 27 . Four of the five sources are quite blue compared to typical lower–redshift dropout galaxies and are clustered within a 1 \sq ^ { \prime } 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 \pm 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 \sim 7 - 8 galaxies as our sample . With the same detection criteria on simulated datasets , assuming no-evolution from z \sim 3.8 , we predict 10 sources at z \sim 7 - 8 , or 14 if we use a more realistic ( 1 + z ) ^ { -1 } size scaling . We estimate that the rest-frame continuum UV ( \sim 1800 \AA ) luminosity density at z \sim 7.5 ( integrated down to 0.3 L _ { z = 3 } ^ { * } ) is just 0.20 _ { -0.08 } ^ { +0.12 } \times that found at z \sim 3.8 ( or 0.20 _ { -0.12 } ^ { +0.23 } \times including cosmic variance ) . Effectively this sets an upper limit on the luminosity density down to 0.3 L _ { z = 3 } ^ { * } . This result is consistent with significant evolution at the bright end of the luminosity function from z \sim 7.5 to z \sim 3.8 . Even with the lower UV luminosity density at z \sim 7.5 , it appears that galaxies could still play an important role in reionization at these redshifts , though definitive measurements remain to be made .