This paper presents a Continuous-Curvature Path Planner (CCPP) for a car-like robot. Existing planners for car-like robots compute paths made up of straight segments connected with tangential circular arcs. The curvature of this type of path is discontinuous (the discontinuities occurring at the transitions between segments and arcs), and when it is time for a car-like robot to actually follow such a path, it has to stop at each transition so as to reorient its front wheels. CCPP is one of the first to compute collision-free paths with continuous curvature profiles. These paths are made up of clothoid arcs (a clothoid is a curve whose curvature is a linear function of its arc length). CCPP uses a general planning technique called the Ariadne's Clew algorithm [mazer:etal:ias:93]. It is based upon two complementary functions: SEARCH and EXPLORE. EXPLORE builds an approximation of the region of the configuration space reachable from a start configuration by incrementally placing a set of reachable landmarks in the configuration space. SEARCH checks the existence of a solution path between a landmark newly placed and the goal configuration.