A two-cell chemical oscillator, based on cubic autocatalysis, is considered, with the reaction in each identical cell being P → A; A + 2B → 3B; B → C. The coupling between the cells is assumed to take place by a linear exchange of either reactant A or autocatalyst B. In the former case, five possible stationary states are found with there being a range of parameter values over which non-symmetric stable stationary states can exist. In the latter case, the only possible stationary state is the same as for the uncoupled system. In both cases, Hopf bifurcations are found, leading to sequences of complex dynamical behaviour