This paper puts forward a location-routing problem with time windows (LRPTW) under uncertainty. It has been assumed that demands of customers and travel times are fuzzy variables. A fuzzy chance constrained programming (CCP) model has been designed using credibility theory and a simulation-embedded simulated annealing (SA) algorithm is presented in order to solve the problem. To initialize solutions of SA, a heuristic method based on fuzzy c-means (FCM) clustering with Mahalanobis distance and sweep method have been employed. The numerical experiments clearly attest that the proposed solution approach is both effective and robust in solving problems with up to 100 demand nodes in reasonable times.