We present a candidate for the most distant galaxy known to date with a
photometric redshift z = 10.7 +0.6 / -0.4 95% confidence limits; with z < 9.5
galaxies of known types ruled out at 7.2-sigma. This J-dropout Lyman Break
Galaxy, named MACS0647-JD, was discovered as part of the Cluster Lensing and
Supernova survey with Hubble CLASH. We observe three magnified images of this
galaxy due to strong gravitational lensing by the galaxy cluster
MACSJ0647.7+7015 at z = 0.591. The images are magnified by factors of ~8, 7,
and 2, with the brighter two observed at ~26th magnitude AB ~0.15 uJy in the
WFC3/IR F160W filter ~1.4 - 1.7 um where they are detected at >~ 12-sigma.
All three images are also confidently detected at >~ 6-sigma in F140W ~1.2 -
1.6 um, dropping out of detection from 15 lower wavelength HST filters ~0.2 -
1.4 um, and lacking bright detections in Spitzer/IRAC 3.6um and 4.5um imaging
~3.2 - 5.0 um. We rule out a broad range of possible lower redshift
interlopers, including some previously published as high redshift candidates.
Our high redshift conclusion is more conservative than if we had neglected a
Bayesian photometric redshift prior. Given CLASH observations of 17 high mass
clusters to date, our discoveries of MACS0647-JD at z ~ 10.8 and MACS1149-JD1
at z ~ 9.6 are consistent with a lensed luminosity function extrapolated from
lower redshifts. This would suggest that low luminosity galaxies could have
reionized the universe. However given the significant uncertainties based on
only two galaxies, we cannot yet rule out the sharp drop off in number counts
at z >~ 10 suggested by field searches.