In this paper we present a new algorithm to find the optimal unit commitment and economic dispatch (UC/D) for a large hydrothermal power system. Mathematically, this is a large nonlinear, mixed integer optimization problem involving over 16,800 integer variables for a system having 100 thermal units with a 1-week scheduling horizon. We use a dual programming approach to solve a separate optimal control problem for each thermal unit and for each set of coupled hydro units. The algorithm has been tested on a 100 thermal unit/6 hydro unit system having a 168-hour scheduling period, and will find solutions that are within 0.1 to 0.25 percent of the optimal dual cost. We report computational results for a system modeled after the New York Power Pool.