Symmetry plays a crucial part in our understanding of the natural world. Mirror symmetry breaking is of special interest as it is related to life as we know it. Studying systems which display chiral amplification, therefore, could further our understanding of symmetry breaking in chemical systems, in general, and thus also of the asymmetry in Nature. Here, we report on strong chiral amplification in the colloidal synthesis of intrinsically chiral lanthanide phosphate nanocrystals, measured via circularly polarized luminescence. The amplification involves spontaneous symmetry breaking into either left- or right-handed nanocrystals below a critical temperature. Furthermore, chiral tartaric acid molecules in the solution direct the amplified nanocrystal handedness through a discontinuous transition between left- and right-handed excess. We analyze the observations based on the statistical thermodynamics of critical phenomena. Our results demonstrate how chiral minerals with high enantiopurity can form in a racemic aqueous environment.