We present the discovery of molecular hydrogen (H-2), including the presence of vibrationally-excited H-2* in the optical spectrum of the of GRB 120815A at z = 2.36 obtained with X-shooter at the VLT. Simultaneous photometric broad-band data from GROND X-ray observations by SwiftXRT place further constraints on the amount and nature of dust along the sightline. The galactic of GRB 120815A is characterized by a strong DLA with log(N(H I) = cm(-2)) = 21.95 +/- 0.10, prominent H-2 absorption the Lyman-Werner bands (log(N(H-2) = cm(-2)) = 20.54 +/- 0.13) and thus a molecular gas fraction log f(H-2) = 1.14 +/- 0.15. The d between the absorbing neutral gas and GRB 120815A is constrained via photo-excitation modeling of fine-structure and stable transitions of Fe II and Ni II to d = 0.5 +/- 0.1 kpc. The DLA metallicity ([Zn = H] = 1.15 +/- 0.12), visual extinction AV less than or similar to 0.15 mag) and dust depletion ([Zn = Fe] = 1.01 +/- 0.10) are intermediate between the values of well-studied, H-2-deficient DLAs observed at high spectral resolution, and the approximately solar metallicity, highly-obscured and H-2-rich GRB 080607 With respect to N(H I), metallicity, as well as dust-extinction and depletion, GRB 120815A is fairly representative of the properties of GRB-DLAs. This demonstrates that molecular hydrogen is present in at least a fraction of the more typical GRB- and H-2 and H-2* are probably more wide-spread among GRB-selected systems than the few examples of previous detections suggest. Because H-2* transitions are located redwards of the Lyman alpha absorption, H-2* opens a second route for positive searches molecular absorption also in GRB afterglows at lower redshifts and observed at lower spectral resolution. Further detections of gas in GRB-DLAs would allow statistical studies, and, coupled with host follow-up and sub-mm spectroscopy, provide insights into the process and conditions of star-formation at high redshift.