Circularly polarized light (CPL) carrying spin angular momentum is crucial to many applications, such as quantum computing, optical communication, novel displays, and biosensing. Nonetheless, the emission from chiral molecules contains comparable CPL components with opposite handedness, resulting in low levels of CPL overall with a small dissymmetry factor and fixed handedness consistent with the handedness of the molecules. Nanoantennas have proved to be useful tools for controlling the emission properties of quantum emitters. In particular, dielectric resonators support electric and magnetic modes, which implies unparalleled opportunities to interact with chiral molecules whose emission originates from both electric and magnetic dipole transitions. In this work, we theoretically study the effects of a spherical dielectric nanoantenna on the directionality and polarization of emission from a chiral molecule. With exact analytical solutions based on generalized Mie theory, we show that directional chiral light emission and nontrivial polarization modulation, such as handedness reversal or chirality enhancement, can be achieved simultaneously for a chiral dipole tangentially coupled with a silicon nanosphere. The influence of the relative strength and orientation between the electric and magnetic dipole moments is also discussed. Our results suggest a new approach to controlling chiral dipolar emission and could benefit the development of chiral light sources.