It was recently discovered that the low-temperature, charge-ordered phase of 1T-TiSe(2) has a chiral character. This unexpected chirality in a system described by a scalar order parameter could be explained in a model where the emergence of relative phase shifts between three charge density wave components breaks the inversion symmetry of the lattice. Here, we present experimental evidence for the sequence of phase transitions predicted by that theory, going from disorder to nonchiral and finally to chiral charge order. Employing x-ray diffraction, specific heat, and electrical transport measurements, we find that a novel phase transition occurs ~7 K below the main charge ordering transition in TiSe(2), in agreement with the predicted hierarchy of charge-ordered phases.