We demonstrate that a high degree of circular polarization can be delivered to the near field (NF) of an aperture at the apex of hollow-pyramid probes for scanning optical microscopy. This result is achieved by analyzing the dichroic properties of an annealed thin polymer film containing a chiral polyfluorene derivative, placed in close proximity to the optical probe. We also prove that the degree of circular polarization in the probe NF does not depend in a significant way on the shape of the aperture, at variance with the far-field behavior. These results demonstrate the feasibility of nano-optics applications exploiting circularly polarized NFs