GRB 080916C is one of only a few gamma-ray bursts (GRBs) known to have many high energy photons — in excess of 200 over 30 MeV and more than 16 over 1 GeV. GRB 080916C is also noteworthy for its high photometric redshift of 4.35. A casual inspection of the arrival times of all Fermi-LAT recorded Pass-8 events from GRB 080916C raised the possibility of short-time scale temporal substructures within the first pulse. Such structures, were they to exist, might be important for analyses of cosmological dispersion measures such as Lorentz invariance violations and the gravitational weak equivalence principle, as well as possibly helping the understanding of how attributes of GRB pulses extend to very high energies. To investigate the reality of these substructures, we carried out a statistical analysis for both Pass-8 events and photons for the entire GRB. The results of our search for substructure down to the millisecond time scale will be reported.