Many strongly correlated materials display quadrupolar (Jahn-Teller) distortion of the local octahedral structural units. It is common for these distortions to be observed by probes of local structure but absent in the crystallographic average structure. The ordering of these quadrupoles is important in determining the properties of manganites and cuprates, and the nature of the disorder in these structures has been an unsolved problem. We combine high resolution scattering data and novel geometrical modeling techniques to obtain a detailed picture of the local atomic structure, and also to extract the quadrupolar order parameter associated with the distorted octahedra. We show that in LaMnO3, quadrupoles undergo a strong first-order phase transition at 730 K, but with nonzero order parameter remaining in the high-temperature phase.