ABSTRACT We present Giant Meterwave Radio Telescope (GMRT) and Westerbork Synthesis Radio Telescope (WSRT) observations of the recently discovered Local Group dwarf galaxy, Leo T. The peak H i column density is measured to be 7 × 1020 cm-2, and the total H i mass is 2.8 × 105 M⊙, based on a distance of 420 kpc. Leo T has both cold (∼500 K) and warm (∼6000 K) H i at its core, with a global velocity dispersion of 6.9 km s-1, from which we derive a dynamical mass within the H i radius of 3.3 × 106 M⊙, and a mass-to-light ratio of >50. We calculate the Jeans mass from the radial profiles of the H i column density and velocity dispersion, and predict that the gas should be globally stable against star formation. This finding is inconsistent with the half light radius of Leo T, which extends to 170 pc, and indicates that local conditions must determine where star formation takes place. Leo T is not only the lowest luminosity galaxy with on-going star formation discovered to date, but it is also the most dark matter-dominated, gas-rich dwarf in the Local Group.