If a gamma-ray burst (GRB) with strong UV emission occurs in a molecular cloud, excitation of the surrounding H-2 will have observable consequences. The UV will pump H-2 into vibrationally excited levels that produce strong absorption at wavelengths lambda less than or similar to 1650 Angstrom. As a result, both the prompt flash and later afterglow will exhibit strong absorption shortward of 1650 % with specific spectroscopic features. Such a cutoff in the emission from GRB 980329 may have already been observed by Fruchter and coworkers; if so, GRB 980329 was at redshift 3.0 less than or similar to z less than or similar to 4.4. BVRI photometry of GRB 990510 could also be explained by H-2 absorption if GRB 990510 was at redshift 1.6 less than or similar to z less than or similar to 2.3. Fluorescence accompanying the UV pumping of the H-2 will result in UV emission from the GRB which can extend over days or months, with 7.5-13.6 eV fluorescent luminosity similar to 10(42) ergs s(-1). Spectroscopy can distinguish this fluorescence from other possible sources of transient optical emission, such as a supernova.