Exoplanet transit surveys have revealed the existence of numerous multi-planetary systems packed close to their stability limit. This feature likely emerges from the formation and dynamical history of the system. Understanding it in detail is thus key to constrain our planet formation scenarios. While the stability limit has been known empirically for decades, no theoretical explanation was proposed yet. I present a mechanism driving the instability of tightly packed system. Based on the chaotic diffusion along the network of three-planet resonances, it reproduces quantitatively the timescale of instability obtained numerically over several order of magnitude in time and planet-to-star mass ratios. I discuss the observational implications of this model, in particular the expected differences between Super-Earths and terrestrial planet systems.