We have searched for interstellar conformer I glycine (NH₂CH₂COOH), the simplest amino acid, in the hot molecular cores Sgr B2(N-LMH), Orion KL, and W51 e1/e2. An improved search strategy for intrinsically weak molecular lines, involving multisource observations, has been developed and implemented. In total, 82 spectral frequency bands, in the millimeter-wave region, were observed over a 4 yr period; 27 glycine lines were detected in 19 different spectral bands in one or more sources. The rotational temperatures derived from "rotation diagrams" are 75 K for Sgr B2(N-LMH), 141 K for Orion KL, and 121 K for W51 e1/e2. The total column densities inferred are 4.16 × 10¹⁴ cm^-2 for Sgr B2, 4.37 × 10¹⁴ cm^-2 for Orion, and 2.09 × 10¹⁴ cm^-2 for W51. Production of interstellar glycine by both gas-phase ion-molecule reactions and by ultraviolet photolysis of molecular ices is briefly discussed. The discovery of interstellar glycine strengthens the thesis that interstellar organic molecules could have played a pivotal role in the prebiotic chemistry of the early Earth.