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