Conditional Moment Closure (CMC) predictions are made for a turbulent jet diffusion flame of a methane-air mixture. They are compared with laser diagnostic measurements for the velocity and mixing fields and temperature and species mass fractions including nitric oxide, NO. in general, results show good agreement for the flow and mixing field, but predictions for the radiation loss from the flame are much higher than those measured directly. Predictions for the conditional average mass fractions of the major species and of the temperature show good agreement with the measurements on the fuel-lean side of stoichiometric. Discrepancies for these quantities are significant on the fuel-rich side and may be due to inadequacies in the chemical mechanisms tested or in the first-order closure used for the chemical reaction rates. Predictions for NO using the thermal mechanism are far too low indicating that prompt mechanism chemistry is needed for adequate predictions. Predictions with the prompt mechanism included are in general too high, probably as a result of inadequate predictions of the fuel-rich side chemistry noted already for the major species.