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 center dot nH(2)O and GlyZI center dot nH(2)O also bind positrons, if their dipole moment mu > mu(cr). However, mu is not a sufficient quantity to describe positron binding to thee complexes. We show that in addition to mu, positron binding strongly depends on the intramolecular bonding of glycine. In Gly center dot H2O, positrons are weakly bound to the nitrogen in Gly, whereas in GlyZI center dot nH(2)O, the ionic oxygen in GlyZI is a strong "positron attractor".