The spectroscopy of O-21 has been investigated using a radioactive O-20 beam and the (d, p) reaction in inverse kinematics. The ground and first excited states have been determined to be J(pi) = 5/2(+) and 1/2(+), respectively. Two neutron unbound states were observed at excitation energies of 4.77(10) and 6.17(11) MeV. The spectroscopic factor deduced for the lower of these, interpreted as a 3/2(+) level, reveals a relatively pure (60%) 0d(3/2) single-particle configuration, in good agreement with shell-model calculations that predict O-26 to be unbound. The large energy difference between the 3/2(+) and 1/2(+) states is indicative of the emergence of the N = 16 shell gap, which is estimated to be 5.1(11) MeV. For the higher-lying resonance, which has a character consistent with a spin-parity assignment of 3/2(+) or 7/2(-), a 0.71(22) branching ratio to the first 2(+) state in O-20 has been observed.