We investigate positron binding to glycine and its aqueous complexes by first-principles calculation. We show that while glycine in its ground state (Gly) does not bind positrons, several of its strongly polar conformers do, and in particular, its zwitterion form (GlyZI) binds positrons strongly. Aqueous complexes Gly·nH2O and GlyZI·nH2O also bind positrons, if their dipole moment μ > μcr. However, μ is not a sufficient quantity to describe positron binding to these complexes. We show that in addition to μ, positron binding strongly depends on the intramolecular bonding of glycine. In Gly·nH2O, positrons are weakly bound to the nitrogen in Gly, whereas in GlyZI·nH2O, the ionic oxygen in GlyZI is a strong "positron attractor".