A search is presented for the decay Y(1S) -> gamma A0, A0 -> cc-bar, where A0 is a candidate for the CP-odd Higgs boson of the next-to-minimal supersymmetric standard model. The search is based on data collected with the BABAR detector at the Y(2S) resonance. A sample of Y(1S) mesons is selected via the decay Y(2S) -> pi+pi-Y(1S). The A0 -> cc-bar decay is identified through the reconstruction of hadronic D0, D+, and D*(2010)+ meson decays. No significant signal is observed. The measured 90% confidence-level upper limits on the product branching fraction B(Y(1S) -> gamma A0) x B(A0 -> cc-bar) range from 7.4 x 10^-5 to 2.4 x 10^-3 for A0 masses from 4.00 to 8.95 GeV/c^2 and 9.10 to 9.25 GeV/c^2, where the region between 8.95 and 9.10 GeV/c^2 is excluded because of background from Y(2S) -> gamma chi_bJ(1P), chi_bJ(1P) -> gamma Y(1S) decays.