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 would allow statistical studies, and, coupled with host follow-up and sub-mm spectroscopy, provide unprecedented insights into the process and conditions of star-formation at high redshift.