The effect of surfactant on the pinch-off of an inviscid bubble surrounded by a viscous fluid is studied theoretically and numerically. Equations governing the evolution of the interface and surfactant concentration in zero-Reynolds-number flow are derived using a long wavelength approximation. In the case of soluble surfactant the derivation assumes either zero bulk Peclet number Pe, or infinite Pe. Results of the long wavelength model are compared against numerical simulations of the full Navier-Stokes equations, performed using an accurate arbitrary Lagrangian-Eulerian method. The presence of insoluble surfactant is found to significantly retard pinch-off. This is due to the development of a long, slender, quasi-steady cylindrical thread at the location of minimum radius, where the destabilizing influence of surface tension is balanced by the internal pressure. For soluble surfactant, depending on parameter values, a thin thread forms first but pinches off later due to the exchange of surfactant between the bulk fluid and the interface.