We provide numerical evidence for the existence of a low-dimensional chaotic attractor in the rheology of dilute suspensions of slender bodies in a simple shear flow. The rheological parameters which characterize the stress deformation behavior of the suspension are calculated based on appropriate averages over the orientation vectors of the slender bodies. The system considered in this work, therefore, exhibits chaos in experimentally measurable averages over a large number of uncoupled chaotic oscillators. The numerical demonstration that these parameters may evolve chaotically may thus have important consequences for both chaos theory and suspension rheology. We also provide plausible explanations for the existence of a low-dimensional chaotic attractor in the rheological parameters in terms of the expressions for the rheological parameters and the coupling between individually chaotically evolving orientations and the expressions for the rheological parameters.