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Artificial nanostructures enable fine control of electromagnetic fields at the nanoscale, a possibility that has recently been extended to the interaction between polarised light and chiral matter. The theoretical description of such interactions, and its application to the design of optimised structures for chiroptical spectroscopies, brings new challenges to the common set of tools used in nano-optics. In particular, chiroptical effects often depend crucially on the relative orientation of the scatterer and the incident light, but many experiments are performed with randomly-oriented scatterers, dispersed in a solution. We derive new expressions for the orientation-averaged local degree of optical chirality of the electromagnetic field in the presence of a nanoparticle aggregate. This is achieved using the superposition T -matrix framework, ideally suited for the derivation of efficient orientation-averaging formulas in light scattering problems. Our results are applied to a few model examples, and illustrate several non-intuitive aspects in the distribution of orientation-averaged degree of chirality around nanostructures. The results will be of significant interest for the study of nanoparticle assemblies designed to enhance chiroptical spectroscopies, and where the numerically-efficient computation of the averaged degree of optical chirality enables a more comprehensive exploration of the many possible nanostructures.