The anionic ring-opening polymerization (AROP) of an azetidine is reported for the first time. The AROP of N-(methanesulfonyl)azetidine (MsAzet), initiated by ⁿBuN(K)Ms, occurs in DMSO at elevated temperatures to form p(MsAzet) as a branched polymer. The polymerization is first order with respect to MsAzet and the number of active chain ends remains constant during the polymerization. Polymer branching occurs due to chain transfer through deprotonation of the methanesulfonyl group, which in turn can initiate a new polymer chain. Evidence for transfer to DMSO is also presented.