We use all available fields with deep NICMOS imaging to search for J _ { 110 } -dropouts ( H _ { 160 ,AB } \lesssim 28 ) at z \approx 10 . Our primary data set for this search were the two J _ { 110 } + H _ { 160 } NICMOS parallel fields taken with the Advanced Camera for Surveys ( ACS ) Hubble Ultra Deep Field ( HUDF ) . The 5 \sigma limiting magnitudes were 28.6 in J _ { 110 } and 28.5 in H _ { 160 } ( 0.6 ^ { \prime \prime } apertures ) . Several shallower fields were also used : J _ { 110 } + H _ { 160 } NICMOS frames available over the Hubble Deep Field ( HDF ) North , the HDF South NICMOS parallel , and the ACS HUDF ( with 5 \sigma limiting magnitudes in J _ { 110 } and H _ { 160 } ranging from 27.0 to 28.2 ) . The primary selection criterion was ( J _ { 110 } - H _ { 160 } ) _ { AB } > 1.8 . Eleven such sources were found in all search fields using this criterion . Eight of these were clearly ruled out as credible z \approx 10 sources , either as a result of detections ( > 2 \sigma ) blueward of J _ { 110 } or their colors redward of the break ( H _ { 160 } - K \sim 1.5 ) ( redder than \gtrsim 98 % of lower redshift dropouts ) . The nature of the 3 remaining sources could not be determined from the data . The number appears consistent with the expected contamination from low-redshift interlopers . Analysis of the stacked images for the 3 candidates also suggests some contamination . Regardless of their true redshifts , the actual number of z \approx 10 sources must be \leq 3 . To assess the significance of these results , two lower redshift samples ( a z \sim 3.8 B -dropout and z \sim 6 i -dropout sample ) were projected to z \sim 8 - 12 using a ( 1 + z ) ^ { -1 } size scaling ( for fixed luminosity ) . They were added to the image frames , and the selection repeated , giving 15.6 and 4.8 J _ { 110 } -dropouts , respectively . This suggests that to the limit of this probe ( \approx 0.3 L _ { z = 3 } ^ { * } ) there has been evolution from z \sim 3.8 and possibly from z \sim 6 . This is consistent with the strong evolution already noted at z \sim 6 and z \sim 7.5 relative to z \sim 3 - 4 . Even assuming that 3 sources from this probe are at z \approx 10 , the rest-frame continuum UV ( \sim 1500 \AA ) luminosity density at z \sim 10 ( integrated down to 0.3 L _ { z = 3 } ^ { * } ) is just 0.19 _ { -0.09 } ^ { +0.13 } \times that at z \sim 3.8 ( or 0.19 _ { -0.10 } ^ { +0.15 } \times including the small effect from cosmic variance ) . However , if none of our sources is at z \approx 10 , this ratio has a 1 \sigma upper limit of 0.07 .