We report on the first observation of cosmologically distant field galaxies
with an high order Adaptive Optics (AO) system on an 8-10 meter class
telescope. Two galaxies were observed at 1.6 microns at an angular resolution
as high as 50 milliarcsec using the AO system on the Keck-II telescope. Radial
profiles of both objects are consistent with those of local spiral galaxies and
are decomposed into a classic exponential disk and a central bulge. A
star-forming cluster or companion galaxy as well as a compact core are detected
in one of the galaxies at a redshift of 0.37+/-0.05. We discuss possible
explanations for the core including a small bulge, a nuclear starburst, or an
active nucleus. The same galaxy shows a peak disk surface brightness that is
brighter than local disks of comparable size. These observations demonstrate
the power of AO to reveal details of the morphology of distant faint galaxies
and to explore galaxy evolution.Comment: 5 pages, Latex, 3 figures. Accepted for publication in P.A.S.