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

Resolving the HI in Damped Lyman-{\alpha} systems that power star-formation