  We present the first detection of molecular hydrogen (H_2) UV absorption
profiles on the line of sight to the LMC. The star LH 10:3120 in the LMC was
measured with the ORFEUS telescope and the Tuebingen echelle spectrograph
during the space shuttle mission of Nov./Dec. 1996. 16 absorption lines from
the Lyman band are used to derive the column densities of H_2 for the lowest 5
rotational states in the LMC gas. For these states we find a total column
density of N(H_2)=6.6 x 10^18$ cm^-2 on this individual line of sight. We
obtain equivalent excitation temperatures of T < 50 K for the rotational ground
state and T = 470 K for 0 < J < 6 by fitting the population densities of the
rotational states to theoretical Boltzmann distributions. We conclude that UV
pumping dominates the population of the higher rotational levels, as known from
the H_2 gas in the Milky Way. (Research supported in part by the DARA)
