We present numerical investigation of the mechanism of surface-enhanced circular dichroism of a chiral medium near nanoantennas. Strong circular dichroism was observed from the chiral medium surrounding nanoantennas with multipolar resonant modes, and the strong circular dichroism was more correlated to the multipolar resonances than to nearfield enhancement or optical helicity enhancement. According to this observation, we suggest multipolar radiative coupling between the nanoantennas and chiral medium as a possible mechanism of the strong chiral response. This work clarifies a mechanism of surface-enhanced chiral responses and would be useful for designing an enantiomeric-sensing platform and realizing devices relying on strong chirality, such as topological metamaterials for scattering-immune propagation of light and negative index metamaterials.