The majority of past work on directed assembly of block copolymers on chemically nanopatterned surfaces (or chemical patterns) has focused on AB diblock copolymers, and the resulting morphologies have generally corresponded to equilibrium states. Here we report a study on directed assembly of ABA triblock copolymers. Directed assembly of thin films of symmetric poly(methyl methacrylate-b-styrene-b-methyl methacrylate) (PMMA-b-PS-b-PMMA) triblock copolymers is shown to be capable of achieving a high degree of perfection, registration, and accuracy on striped patterns having periods, Ls, commensurate with the bulk period of the copolymer, Lo. When Ls is incommensurate with Lo, the triblock copolymer domains can reach dimensions up to 55% larger or 13% smaller than Lo. The range over which triblock copolymers tolerate departures from a commensurate Ls is significantly larger than that accessible with the corresponding diblock copolymer material on analogous directed assembly systems. The assembly kinetics of the triblock copolymer is approximately 3 orders of magnitude slower than observed in the diblock system. Theoretically informed simulations are used to interpret our experimental observations; a thermodynamic analysis reveals that triblocks can form highly ordered, non-equilibrium metastable structures that do not arise in the diblock.Keywords: block copolymer lithography; directed assembly; simulation; thin film; triblock copolymer