  We explore the potential offered by large-mass Liquid Argon detectors for
determination of the sign of Delta m_{31}^2, or the neutrino mass hierarchy,
through interactions of atmospheric neutrinos. We give results for a 100 kT
sized magnetized detector which provides separate sensitivity to \nu_\mu,
\bar{\nu}_\mu and, over a limited energy range, to \nu_e, \bar{\nu}_e.We also
discuss the sensitivity for the unmagnetized version of such a detector. After
including the effect of smearing in neutrino energy and direction and
incorporating the relevant statistical,theoretical and systematic errors, we
perform a binned \chi^2 analysis of simulated data. The \chi^2 is marginalized
over the presently allowed ranges of neutrino parameters and determined as a
function of \theta_{13}. We find that such a detector offers superior
capabilities for hierarchy resolution, allowing a > 4\sigma determination for a
100 kT detector over a 10 year running period for values of \sin^2 2\theta_{13}
\ge 0.05. For an unmagnetized detector, a 2.5\sigma hierarchy sensitivity is
possible for \sin^2 2\theta_{13} = 0.04.
