Amines, particularly primary amines (R-NH2), are closely related to the primordial synthesis of amino acids since they share the same structural backbone. However, only a limited number of amines has been identified in the interstellar medium, which prevents us from studying their chemistry as well as their relation to prebiotic species that could lead to the emergence of life. In this Letter, we report the first interstellar detection of vinylamine (C2H3NH2) and tentative detection of ethylamine (C2H5NH2) toward the Galactic center cloud G+0.693-0.027. The derived abundance with respect to H2 is (3.3 0.4) 10-10 and (1.9 0.5) 10-10, respectively. The inferred abundance ratios of C2H3NH2 and C2H5NH2 with respect to methylamine (CH3NH2) are ∼0.02 and ∼0.008, respectively. The derived abundance of C2H3NH2, C2H5NH2, and several other NH2-bearing species are compared to those obtained toward high-mass and low-mass star-forming regions. Based on recent chemical and laboratory studies, possible chemical routes for the interstellar synthesis of C2H3NH2 and C2H5NH2 are discussed.