The local orientational order between phenylene groups and between carbonate groups in the glassy polycarbonate of 2,2-bis(4-hydroxyphenyl)propane (bisphenol-A) has been studied using C-13 polarization-transfer NMR under slow magic-angle sample spinning. Preferred orientations between neighboring groups have been determined from the rate constant of polarization transfer, measured as a function of the resonance frequencies in two-dimensional experiments. Nearest neighbor phenylene groups tend to have small angles between their longitudinal axes. Nearest neighbor carbonate groups can have parallel and perpendicular directions defined by the pairs of ether oxygens in each group. The perpendicular arrangements are incompatible with existing models of locally parallel chains. The packing characteristics unraveled by NMR are also compared to those of atomistically detailed simulations of bisphenol-A polycarbonate. The atomistic simulations do not reproduce well the local order measured between phenylene groups. However, they account for the occurrence of parallel and perpendicular chain segments with close carbonate groups.