It has been shown that sets of oscillators in a modular network can exhibit a rich variety of metastable chimera states, in which synchronisation and desynchronisation coexist. Independently, under the guise of integrated information theory, researchers have attempted to quantify the extent to which a complex dynamical system presents a balance of integrated and segregated activity. In this paper we bring these two areas of research together by showing that the system of oscillators in question exhibits a critical peak of integrated information that coincides with peaks in other measures such as metastability and coalition entropy.