We study rapidly-rotating turbulent flows in a highly elongated domain using an asymp-totic expansion at simultaneously large rotation rate Ω = O(1/) and domain height H = O(1/), 1. We solve the resulting equations using an extensive set of direct numerical simulations for different parameter regimes. As a parameter λ ∝ Ω/H is increased beyond a threshold λ c , a transition is observed from a state without an inverse energy cascade to a state with an inverse energy cascade. For large Reynolds number and large horizontal box size, we provide evidence for criticality of the transition in terms of the large-scale energy dissipation rate and estimate a critical exponent close to unity.