  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.
