Coherent oscillations of neural activity are ubiquitous across brain spatial and temporal scales and have been associated with the formation of sensory or behavioral representations [1]. Refined experimental techniques report today a new complexity of this oscillatory activity, especially in the gamma (30-100 Hz) band. Indeed, the frequency of these oscillations shows a large variability through time [2], questioning the classical view of γ oscillations being separated into different frequency bands. Oscillations appear instead in bursts characterised by rapid, synchronous neuronal firing. This is difficult to reconcile with often employed massive trial averages or with predictions from simplified computational models. In this work, I will present a new mechanisms for the emergence of bursting gamma oscillations, based on chaotic attractors in spiking networks of excitatory and inhibitory neurons. We also employ a neural mass model to reduce the dimensionality of the network, allowing us to discover a rich repertoire of dynamical phases, from bistable regimes to classical PING periodic oscillations to gamma bursts. We then study the Phase Amplitude Coupling (PAC) of gamma oscillations with a theta forcing across the phase space of the model. We show that PAC is maximum at the edge of this new bursting gamma region. This demonstrates that chaotic oscillatory bursts are capable of boosting information transfer between different neural rhythms. Altogether, we present a theoretical framework to explore the mechanisms of theta-gamma PAC and their relation with the activation of neuronal ensembles.