  We present a technique to identify optical counterparts of 250 um-selected
sources from the Herschel-ATLAS survey. Of the 6621 250 um > 32 mJy sources in
our science demonstration catalogue we find that ~60 percent have counterparts
brighter than r=22.4 mag in the Sloan Digital Sky Survey. Applying a likelihood
ratio technique we are able to identify 2423 of the counterparts with a
reliability R > 0.8. This is approximately 37 percent of the full 250 micron
catalogue. We have estimated photometric redshifts for each of these 2423
reliable counterparts, while 1099 also have spectroscopic redshifts collated
from several different sources, including the GAMA survey. We estimate the
completeness of identifying counterparts as a function of redshift, and present
evidence that 250 um-selected Herschel-ATLAS galaxies have a bimodal redshift
distribution. Those with reliable optical identifications have a redshift
distribution peaking at z ~ 0.25 +/- 0.05, while sub-mm colours suggest that a
significant fraction with no counterpart above the r-band limit have z > 1. We
also suggest a method for selecting populations of strongly-lensed high
redshift galaxies. Our identifications are matched to UV--NIR photometry from
the GAMA survey, and these data are available as part of the Herschel-ATLAS
public data release.
