A nonlinear model predictive control (NMPC) algorithm is developed and tested on the Tennessee Eastman challenge process. The model used in NMPC is a nonlinear, mechanistic, state variable formulation with 26 states, 10 manipulated variables and 23 outputs. Fifteen unmeasured disturbances and parameters are estimated on-line to eliminate offset in outputs. The NMPC strategy controls eight outputs using eight manipulated variables. There is an additional SISO loop to control reactor liquid level. In direct comparisons, we show that NMPC is always superior to a typical SISO multiloop strategy. There are marked improvements in cases involving large changes in setpoints and/or constraint handling. The NMPC algorithm is similar to previous work, but simplifications in the projection/optimization step make the computations more feasible for a typical process computer.