We determine the abundance of i ^ { \prime } -band drop-outs in the recently-released HST /ACS Hubble Ultra Deep Field ( UDF ) . Since the majority of these sources are likely to be z \approx 6 galaxies whose flux decrement between the F775W i ^ { \prime } -band and F850LP z ^ { \prime } -band arises from Lyman-alpha absorption , the number of detected candidates provides a valuable upper limit to the unextincted star formation rate at this redshift . We demonstrate that the increased depth of UDF enables us to reach an 8 \sigma limiting magnitude of z ^ { \prime } _ { AB } = 28.5 ( equivalent to 1.5 h ^ { -2 } _ { 70 } M _ { \odot } { yr } ^ { -1 } at z = 6.1 , or 0.1 L ^ { * } _ { UV } for the z \approx 3 U -drop population ) , permitting us to address earlier ambiguities arising from the unobserved form of the luminosity function . We identify 54 galaxies ( and only one star ) at z ^ { \prime } _ { AB } < 28.5 with ( i ^ { \prime } - z ^ { \prime } ) _ { AB } > 1.3 over the deepest 11 arcmin ^ { 2 } portion of the UDF field . The characteristic luminosity ( L ^ { * } ) is consistent with values observed at z \approx 3 . The faint end slope ( \alpha ) is less well constrained , but is consistent with only modest evolution . The main change appears to be in the number density ( \Phi ^ { * } ) . Specifically , and regardless of possible contamination from cool stars and lower redshift sources , the UDF data support our previous result that the star formation rate at z \approx 6 was approximately \times 6 less than at z \approx 3 ( Stanway , Bunker & McMahon 2003 ) . This declining comoving star formation rate ( 0.005 h _ { 70 } M _ { \odot } { yr } ^ { -1 } { Mpc } ^ { -3 } at z \approx 6 at L _ { UV } > 0.1 L ^ { * } for a salpeter IMF ) poses an interesting challenge for models which suggest that L _ { UV } > 0.1 L ^ { * } star forming galaxies at z \simeq 6 reionized the universe . The short-fall in ionizing photons might be alleviated by galaxies fainter than our limit , or a radically different IMF . Alternatively , the bulk of reionization might have occurred at z \gg 6 .