We initiate a systematic, non-perturbative study of the large-N expansion in the two-dimensional SU(N)×SU(N) principal Chiral model (PCM). 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 we explicitly compute, 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 noncritical string theory and suggests that the double-scaled PCM is dual to a noncritical string with a (2+1)-dimensional target space where an additional dimension emerges dynamically from the SU(N) Dynkin diagram.