Quantum-confined nanostructures of CsPbBr 3 with luminescence quantum efficiencies approaching unity have shown tremendous potential for lighting and quantum light applications. In contrast to CsPbBr 3 quantum dots, where the fine structure of the emissive exciton state has been intensely discussed, the relationship among lattice orientation, shape anisotropy, and exciton fine structure in lead halide nanoplatelets has not yet been established. In this work, we investigate the fine structure of the bright triplet exciton of individual CsPbBr 3 nanoplatelets by polarization-resolved micro-and magnetophotoluminescence spectroscopy at liquid helium temperature and find a large zero-field splitting of up to 2.5 meV. A unique relation between the crystal structure and the photoluminescence emission confirms the existence of two distinct crystal configurations in such nanoplatelets with different alignments of the crystal axes with respect to the nanoplatelet facets. Polarization-resolved experiments eventually allow us to determine the absolute orientation of an individual nanoplatelet on the substrate purely by optical means.