  Proof of the existence of a significant population of normal disk galaxies at
redshift z>2 would have profound implications for theories of structure
formation and evolution. We present evidence based on Keck HIRES observations
that the damped Lyman-alpha absorber at z=3.15 toward the quasar Q2233+1310 may
well be such an example. Djorgovski et al have recently detected the
Lyman-alpha emission from the absorber, which we assume is at the systemic
redshift of the absorbing galaxy. By examining the profiles of the metal
absorption lines arising from the absorbing galaxy in relation to its systemic
redshift, we find strong kinematical evidence for rotation. Therefore the
absorber is likely to be a disk galaxy. The inferred circular velocity for the
galaxy is >200 km/s. With a separation of ~17 kpc between the galaxy and the
quasar sightline, the implied dynamic mass for the galaxy is >1.6x10(11) solar
mass. The metallicity of the galaxy is found to be [Fe/H]=-1.4, typical of
damped Lyman-alpha galaxies at such redshifts. However, in another damped
galactic rotation is evident. In the latter case, the damped Lyman-alpha
absorber occurs near the background quasar in redshift so its properties may be
influenced by the background quasar. These represent the only two cases at
present for which the technique used here may be applied. Future applications
of the same technique to a large sample of damped Lyman-alpha galaxies may
allow us to determine if a significant population of disk galaxies already
existed only a few billion years after the Big Bang.
