The goal of this research is to enable a multi-limbed robot to climb vertical rock using techniques similar to those developed by human climbers. The robot consists of a small number of articulated limbs. Only the limb end-points can make contact with the environment---a vertical surface with small, arbitrarily distributed features called holds. A path through this environment is a sequence of one-step climbing moves in which the robot brings a limb end-point to a new hold.