This paper presents a Monte Carlo technique for sampling configurations of a kinematic chain according to a specified probability density while accounting for loop closure constraints. A key contribution is a method for sampling sub-loops in unbiased fashion using analytical inverse kinematics techniques. Sub-loops are then iterated across the chain to produce samples for the entire chain. The method is demonstrated to scale well to high-dimensional chains (>200DOFs) and is applied to flexible 2D chains, protein molecules, and robots with multiple closed-chains. © 2013 IEEE.