I will present a systematic, non-perturbative analysis of the two-dimensional SU(N) Principal Chiral Model (PCM) in the large-N limit. Starting with the known infinite-N solution for the ground state at fixed chemical potential, we devise an iterative procedure to solve the Bethe ansatz equations order by order in 1/N. The first few orders, which are explicitly computed, reveal a systematic enhancement pattern at strong coupling calling for the near-threshold resummation of the large-N expansion. The resulting double-scaling limit bears striking similarities to the c=1 non-critical string theory and suggests that the double-scaled PCM is dual to a non-critical string with a 2+1-dimensional target space where an additional dimension emerges from the SU(N) Dynkin diagram.