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We present the discovery of molecular hydrogen (H_2), including the presenceof vibrationally-excited H_2^* in the optical spectrum of the afterglow of GRB120815A at z=2.36 obtained with X-shooter at the VLT. Simultaneous photometricbroad-band data from GROND and X-ray observations by Swift/XRT place furtherconstraints on the amount and nature of dust along the sightline. The galacticenvironment of GRB 120815A is characterized by a strong DLA withlog(N(H)/cm^-2) = 21.95 +/- 0.10, prominent H_2 absorption in the Lyman-Wernerbands (log(N(H_2)/cm^-2) = 20.53 +/- 0.13) and thus a molecular gas fractionlog f(H_2)=-1.14 +/- 0.15. The distance d between the absorbing neutral gas andGRB 120815A is constrained via photo-excitation modeling of fine-structure andmeta-stable transitions of FeII and NiII to d = 0.5 +/- 0.1 kpc. The DLAmetallicity ([Zn/H] = -1.15 +/- 0.12), visual extinction (A_V < 0.15 mag) anddust depletion ([Zn/Fe] = 1.01 +/- 0.10) are intermediate between the values ofwell-studied, H_2-deficient GRB-DLAs observed at high spectral resolution, andthe approximately solar metallicity, highly-obscured and H_2-rich GRB 080607sightline. With respect to N(H), metallicity, as well as dust-extinction anddepletion, GRB 120815A is fairly representative of the average properties ofGRB-DLAs. This demonstrates that molecular hydrogen is present in at least afraction of the more typical GRB-DLAs, and H_2 and H_2^* are probably morewide-spread among GRB-selected systems than the few examples of previousdetections would suggest.

Molecular Hydrogen in the Damped Lyman-alpha System towards GRB 120815A at z=2.36