We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument. mean-Held calculation and Monte Carlo simulations, we show that at a critical pressure. Pc ∼ N-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N2. The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which) 〈A〉 N3/2. For p > pc we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.