We present high spatial resolution (51 × 27) Owens Valley Radio Observatory (OVRO) millimeter array observations of HCN (J = 1-0) and HCO+ (J = 1-0) emission in the inner 3 pc of the Galaxy (0.04 pc ~ 1''). The HCN and HCO+ emission of the circumnuclear disk (CND) is distributed in a well-defined ring with a peak at a radius of 1.6 pc. The observed radial velocities are generally consistent with rotation at ~110 km s-1 (except along the western edge of the CND). The HCO+/HCN emission ratio is typically ~0.4 but with significant variations. The variations in the HCO+/HCN emission and absorption ratios can be attributed to greater abundances of HCO+ in lower density regions both within the CND and along the line of sight. The HCN emission is well correlated with the H2 emission at 2.12 μm both in the main emission lobes of the CND and also in four H2 and HCN filaments. Multiple areas of interaction between the ionized gas and the CND are also seen; the western arm of the minispiral is spatially and kinematically consistent with being the ionized inner edge of the CND, and the northern arm may be connected to the CND northeastern extension. With the enhanced spatial resolution of the HCN maps, we resolve numerous dense molecular gas cores within the CND with characteristic diameter ~7'' (0.25 pc). For 26 of the more isolated cores, we have measured sizes, velocity widths, and integrated fluxes. From these properties we estimated three masses for each core: a virial mass assuming the cores are gravitationally bound, an optically thick mass from observed column densities of HCN, and a lower limit mass assuming the HCN emission is optically thin and shock excitation is negligible. The virial and optically thick masses are in good agreement with a typical mass of (2-3) × 104 M and a total CND gas mass of 106 M. The internal densities implied by these core masses (assuming a uniform density distribution for each core) are on average (3-4) × 107 cm-3. The core densities are high enough to be stable against tidal disruption from Sgr A* and the central stellar concentration. This tidal stability suggests a longer lifetime for the CND. The high densities and masses within the cores might support star formation either in the CND itself or within a core infalling toward the inner parsec, thus providing a mechanism for the formation of the young stellar population observed in the inner arcseconds of the Galaxy.