We present a sample of 16 robust z \sim 7 z _ { 850 } -drop galaxies detected by the newly installed WFC3/IR camera on the Hubble Space Telescope . Our analysis is based on the first epoch data of the HUDF09 program covering the Hubble Ultra Deep Field with 60 orbits of Y _ { 105 } , J _ { 125 } , and H _ { 160 } observations . These remarkable data cover 4.7 arcmin ^ { 2 } and are the deepest NIR images ever taken , reaching to \sim 29 mag AB ( 5 \sigma ) . The 16 z \sim 6.5 - 7.5 galaxies have been identified based on the Lyman Break technique utilizing ( z _ { 850 } - Y _ { 105 } ) vs. ( Y _ { 105 } - J _ { 125 } ) colors . They have magnitudes J _ { 125 } = 26.0 - 29.0 ( AB ) , an average apparent half-light radius of \sim 0.16 arcsec ( \lesssim 1 kpc ) , and show very blue colors ( some even \beta \lesssim - 2.5 ) , in particular at low luminosities . The WFC3/IR data confirms previous NICMOS detections indicating that the dropout selection at z \sim 7 is very reliable . Our data allow a first determination of the faint end slope of the z \sim 7 luminosity function , reaching down to M _ { UV } \sim - 18 , a full magnitude fainter than previous measurements . When fixing \phi _ { * } = 1.4 \times 10 ^ { -3 } Mpc ^ { -3 } mag ^ { -1 } to the value previously measured at z \sim 6 , we find a best-fit value of \alpha = -1.77 \pm 0.20 , with a characteristic luminosity of M _ { * } = -19.91 \pm 0.09 . This steep slope is similar to what is seen at z \sim 2 - 6 and indicates that low luminosity galaxies could potentially provide adequate flux to reionize the universe . The remarkable depth and resolution of these new images provide insights into the coming power of JWST .