In this talk, an optimization method for nonsmooth locally Lipschitz functions on Riemannian manifolds will be presented. The method is based on approximating the subdifferential of the cost function at every iteration by the convex hull of transported gradients from tangent spaces at randomly generated nearby points to the tangent space of the current iterate, and can hence be seen a generalization of the well-known gradient sampling algorithm to a Riemannian setting. A convergence result will be obtained under the assumption that the cost function is continuously differentiable on an open set of full measure, and that the employed vector transport and retraction satisfy certain conditions, which hold for instance for the exponential map and parallel transport. Then with probability one the algorithm is feasible, and either the sequence of function values associated with the constructed iterates is unbounded from below, or each cluster point of the iterates is a Clarke stationary point.