Nanocrystal quantum dot (NQD) fluorescence in 1-D glassy cholesteric liquid crystal host is investigated: (1) Microcavity resonance is obtained under cw-excitation demonstrating coupling between NQD fluorescence and a cholesteric microcavity. Observed at a band edge of a photonic stopband, this resonance has circular polarization due to microcavity chirality with 4.9times intensity enhancement in comparison with polarization of the opposite handedness. (2) Photon antibunching of a single NQD in a similar microcavity was observed. (3) Fluorescence decay time constants were measured at different excitation powers. These results are important in developing cholesteric lasers and single-photon sources for secure quantum communication.