  We present high resolution observations of an extremely metal-poor damped
Lyman-alpha system, at z_abs = 2.3400972 in the spectrum of the QSO J0035-0918,
exhibiting an abundance pattern consistent with model predictions for the
supernova yields of Population III stars. Specifically, this DLA has [Fe/H] =
-3.04, shows a clear `odd-even' effect, and is C-rich with [C/Fe] = +1.53, a
factor of about 20 greater than reported in any other damped Lyman-alpha
system. In analogy to the carbon-enhanced metal-poor stars in the Galactic halo
(with [C/Fe] > +1.0), this is the first reported case of a carbon-enhanced
damped Lyman-alpha system. We determine an upper limit to the mass of 12C,
M(12C) < 200 solar masses, which depends on the unknown gas density n(H); if
n(H) > 1 atom per cubic cm (which is quite likely for this DLA given its low
velocity dispersion), then M(12C) < 2 solar masses, consistent with pollution
by only a few prior supernovae. We speculate that DLAs such as the one reported
here may represent the `missing link' between the yields of Pop III stars and
their later incorporation in the class of carbon-enhanced metal-poor stars
which show no enhancement of neutron-capture elements (CEMP-no stars).
