Chaining, in combination with adaptive importance sampling, can provide an effective technique for the numerical evaluation of high-dimensional integrals in the context of a posterior analysis. In many statistical problems ways of applying chaining can be found which depend heavily on the structure of the problem. In this paper we consider a very general method of implementing chaining for arbitrary integrals. Also, we show that chaining can be applied to solve global optimization problems and prove several generalizations of a theorem of Pincus.