Small spherical guest particles added to a nematic liquid-crystalline dispersion of colloidal rods self-assemble linearly into chain-like aggregates. We argue that the formation of these chains is induced by the excluded-volume coupling of the globules to the nematic matrix, and that pretransitional fluctuations in the mixture give rise to the structural reorganization of the linear aggregates observed in experiment. Ultimately, the repulsive interactions between the globules and the rods either promote large-scale demixing or a transition to a microphase-separated lamellar state, depending on the concentration of rods in the host dispersion.