  Reservoirs of dense atomic gas (primarily hydrogen), contain approximately 90
percent of the neutral gas at a redshift of 3, and contribute to 2-3 percent of
the total baryons in the Universe. These damped Lyman-${\alpha}$ systems (so
called because they absorb Lyman-${\alpha}$ photons from within and from
background sources) have been studied for decades, but only through absorption
lines present in the spectra of background quasars and gamma-ray bursts. Such
pencil beams do not constrain the physical extent of the systems. Here, we
report integral-field spectroscopy of a bright, gravitationally lensed galaxy
at a redshift of 2.7 with two foreground damped Lyman-${\alpha}$ systems. These
systems are $>$ 238 $kpc^2$ in extent, with column densities of neutral
hydrogen varying by more than an order of magnitude on $<$ 3 kpc-scales. The
mean column densities are $10^{20.46}$ - $10^{20.84} cm^{-2}$ and the total
masses are $> 5.5 \times 10^{8}$ - $1.4 \times 10^{9} M_{\odot}$, showing that
they contain the necessary fuel for the next generation of star formation,
consistent with relatively massive, low-luminosity primeval galaxies at
redshifts $>$ 2.
