Abstract A model of dynamical holes in a planar quantum antiferromagnet is analysed in the limit of large spin and small doping concentration. The long-wavelength limit of this system is found to be a relativistic QFT of multiflavour Dirac fermions with both four-fermion and statistical chiral gauge interactions. The Schwinger-Dyson equation for the fermion self-energy is solved in the limit of many flavours and the theory is found to possess a phase in which the global vector symmetry of the effective action is realised in the Kosterlitz-Thouless mode. The theory exhibits superconductivity without parity or time-reversal violation in this phase and the charge quantum assumes the phenomenologically relevant value of 2 e. The mechanism is conjectured to be “hole-pair” condensation due primarily to the statistical gauge interaction. Although there is a formal similarity with BCS theory the physical origin of the attraction between holes is quite different. The model may provide a prototype for further studies in realistic microscopic systems that attempt to simulate planar high temperature superconducting oxides.