We have grown a novel crystal of hydrated gycylglycine (Gly-Gly), determined its crystal structure, and measured its Raman tensor at 488, and 244 nm, close to resonance. This crystal has 8 molecules of (Gly-Gly) and 12 molecules of water per unit cell. The Gly-Gly hydrogen-bonds in a beta-sheet-like structure where all of the amide planes are parallel. We report here the development of a general method to use preresonance single-crystal Raman measurements to determine the direction of the molecular electronic transition moments. We utilize the UV (244 nm) excited Raman tensor and relationships derived here to accurately determine the transition moment orientation of the amide and carboxylate group pi-->pi* transitions and the orientation of a charge transfer transition from the carboxylate group to the amide group. The amide pi-->pi* (NV’(l)) transition moment is found to be in the peptide plane at an angle of -46 degrees +/- 3 degrees to the amide carbonyl bond. The carboxylate pi-->pi* (NV’(l)) transition moment is oriented almost parallel to a line connecting the carboxylate oxygens (4.6 degrees off), as theoretically expected. The charge transfer band from the carboxylate to the amide chromophore is found at an angle of -83 degrees +/- 3 degrees to the amide carbonyl bond, almost along the line of intersection of the amide and carboxylate planes.