We experimentally investigate the collective behaviour of four turbulent lean-premixed combustors coupled in a ring network. We adopt a complex systems approach, treating each combustor as an individual self-excited thermoacoustic oscillator and examining how a minimal network of such oscillators can transition into synchronous and asynchronous states. Using synchronization metrics, we identify a broad range of collective behaviour, including a weak anti-phase chimera, a breathing chimera, intermittent frequency locking, and three-frequency quasiperiodicity. The discovery of chimera states in a minimal network of coupled thermoacoustic oscillators suggests that chimera control techniques could be exploited for the suppression of thermoacoustic oscillations in can-annular combustion systems.