We present Giant Meterwave Radio Telescope (GMRT) and Westerbork ynthesis Radio Telescope (WSRT) observations of the recently discovered Local Group dwarf galaxy, Leo T. The peak HI column density is measured to be 7x10^20 cm^-2, and the total HI mass is 2.8Xx10^5 Msun, based on a distance of 420 kpc. Leo T has both cold (~ 500 K) and warm (~ 6000 K) HI at its core, with a global velocity dispersion of 6.9 km/s, from which we derive a dynamical mass within the HI radius of 3.3x10^6 Msun, and a mass-to-light ratio of greater than 50. We calculate the Jeans mass from the radial profiles of the HI 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, it is also the most dark matter dominated, gas-rich dwarf in the Local Group.