  GRB 080607 has provided the first strong observational signatures of
molecular absorption bands toward any galaxy hosting a gamma-ray burst. Despite
the identification of dozens of features as belonging to various atomic and
molecular (H_2 and CO) carriers, many more absorption features remained
unidentified. Here we report on a search among these features for absorption
from vibrationally-excited H_2, a species that was predicted to be produced by
the UV flash of a GRB impinging on a molecular cloud. Following a detailed
comparison between our spectroscopy and static, as well as dynamic, models of
H_2* absorption, we conclude that a column density of 10^{17.5+-0.2} cm^{-2} of
H_2* was produced along the line of sight toward GRB 080607. Depending on the
assumed amount of dust extinction between the molecular cloud and the GRB, the
model distance between the two is found to be in the range 230--940 pc. Such a
range is consistent with a conservative lower limit of 100 pc estimated from
the presence of Mg I in the same data. These distances show that substantial
molecular material is found within hundreds of pc from GRB 080607, part of the
distribution of clouds within the GRB host galaxy.
