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It has been long recognized that the spatial polarization of the electronic clouds in molecules, and the spatial arrangements of atoms into chiral molecular structures, play crucial roles in physics, chemistry and biology. However, these two fundamental concepts - chirality and polarization - have remained unrelated so far. This work connects them by introducing and exploring the concept of polarization of chirality. We show that, like charge, chirality, or handedness, can be polarized, and that such polarization leads to fundamental consequences, demonstrated here using light. First, we analyze how chirality dipoles and higher-order chirality multipoles manifest in experimental observables. Next, we show how to create chirality-polarized optical fields of alternating handedness in space. Despite being achiral, these racemic space-time light structures interact differently with chiral matter of opposite handedness, and the chirality dipole of light controls and quantifies the strength of the enantio-sensitive response. Using nonlinear interactions, we can make a medium of randomly oriented chiral molecules emit light to the left, or to the right, depending on the molecular handedness and on the chirality dipole of light. The chiral dichroism in emission direction reaches its highest possible value of 200%. Our work opens the field of chirality polarization shaping of light and new opportunities for efficient chiral discrimination and control of chiral and chirality-polarized light and matter on ultrafast time scales.