This paper presents a general framework for planning the quasi-static motion of a three-limbed climbing robot in vertical natural terrain. The problem is to generate a sequence of continuous one-step motions between consecutive holds that will allow the robot to reach a particular goal hold. A detailed algorithm is presented to compute a one-step motion considering the equilibrium constraint only. The overall framework combines this local planner with a heuristic search technique to generate a complete plan. An online implementation of the algorithm is demonstrated in simulation.