  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.
