We present a compositional approach to controller synthesis of discrete event system controllers with linear temporal logic (LTL) goals. We exploit the modular structure of the plant to be controlled, given as a set of labelled transition systems (LTS), to mitigate state explosion that monolithic approaches to synthesis are prone to. Maximally permissive safe controllers are iteratively built for subsets of the plant LTSs by solving weaker control problems. Observational synthesis equivalence is used to reduce the size of the controlled subset of the plant by abstracting away local events. The result of synthesis is also compositional, a set of controllers that when run in parallel ensure the LTL goal. We implement synthesis in the MTSA tool for an expressive subset of LTL, GR(1), and show it computes solutions to that can be up to 1000 times larger than those that the monolithic approach can solve.