The Lyman Continuum photon production efficiency ($xi_{rm ion}$) is a critical ingredient for inferring the number of photons available to reionise the intergalactic medium. To estimate the theoretical production efficiency in the high-redshift Universe we couple the BlueTides cosmological hydrodynamical simulation with a range of stellar population synthesis models. We find Lyman Continuum photon production efficiencies of $log_{10}(xi_{rm ion}/{rm erg^{-1}, Hz})approx 25.1-25.5$ depending on the choice of stellar population synthesis model. These results are broadly consistent with recent observational constraints at high-redshift though favour a model incorporating the effects of binary evolution