We enhance the weak optical signals of small chiral molecules via circular differential Mie scattering (CDMS) of nanoparticles immersed in them. CDMS is the preferential Mie scattering of left- and right-handed circularly polarized light by nanoparticles whose sizes are about the same as the wavelength of light. Solving the Mie scattering theory for chiral media, we find that the CDMS signal of the particle is linearly proportional to the chirality parameter κ of the molecules. This linear amplitude enhancement by CDMS of the particle holds, even for large particles, which have a retardation effect. We also demonstrate that the CDMS of a nanoparticle is sensitive to changes of molecular concentration, and that the nanoparticle can be utilized as a chiroptical biosensor detecting the concentration of analyte. We expect that the enhancement of molecular chiroptical signals by CDMS will pave the way for novel chiroptical spectroscopy using nanostructures.