We have searched for star-forming galaxies at z \approx 7 - 10 by applying the Lyman-break technique to newly-released Y - , J - & H -band images ( 1.1 , 1.25 , 1.6 \mu m ) from WFC3 on the Hubble Space Telescope . By comparing these images of the Hubble Ultra Deep Field with the ACS z ^ { \prime } -band ( 0.85 \mu m ) images , we identify objects with red colours , ( z ^ { \prime } - Y ) _ { AB } > 1.3 , consistent with the Lyman- \alpha forest absorption at z \approx 6.7 - 8.8 . We identify 12 of these z ^ { \prime } -drops down to a limiting magnitude Y _ { AB } < 28.5 ( equivalent to a star formation rate of 1.3 M _ { \odot } { \mathrm { y } r } ^ { -1 } at z = 7.1 ) , all of which are undetected in the other ACS filters . We use the WFC3 J -band image to eliminate contaminant low mass Galactic stars , which typically have redder colours than z \approx 7 galaxies . One of our z ^ { \prime } -drops is a probably a T-dwarf star . The z \approx 7 z ^ { \prime } -drops appear to have much bluer spectral slopes than Lyman-break galaxies at lower redshift . Our brightest z ^ { \prime } -drop is not present in the NICMOS J -band image of the same field taken 5 years before , and is a possible transient object . From the 10 remaining z \approx 7 candidates we determine a lower limit on the star formation rate density of 0.0017 M _ { \odot } { \mathrm { y } r } ^ { -1 } { \mathrm { M } pc } ^ { -3 } for a Salpeter initial mass function , which rises to 0.0025 - 0.004 M _ { \odot } { \mathrm { y } r } ^ { -1 } { \mathrm { M } pc } ^ { -3 } after correction for luminosity bias . The star formation rate density is a factor of \approx 10 less than that of Lyman-break galaxies at z = 3 - 4 , and is about half the value at z \approx 6 . We also present the discovery of 7 Y -drop objects with ( Y - J ) _ { AB } > 1.0 and J _ { AB } < 28.5 which are candidate star-forming galaxies at higher redshifts ( z \approx 8 - 9 ) . We find no robust J -drop candidates at z \approx 10 . While based on a single deep field , our results suggest that this star formation rate density would produce insufficient Lyman continuum photons to reionize the Universe unless the escape fraction of these photons is extremely high ( f _ { \mathrm { e } sc } > 0.5 ) , and the clumping factor of the Universe is low . Even then , we need to invoke a large contribution from galaxies below our detection limit ( a steep faint end slope ) . The apparent shortfall in ionizing photons might be alleviated if stellar populations at high redshift are low metallicity or have a top-heavy initial mass function .