A lattice ribbon is a connected sequence of plaquettes subject to certain selfavoidance conditions. The ribbon can be closed to form an object which is topologically either a cylinder or a M6bius band, depending on whether its surface is orientable or nonorientable. We describe a grand canonical Monte Carlo algorithm for generating a sample of these ribbons, prove that the associated Markov chain is ergodic, and present and discuss numerical results about the dimensions and entanglement complexity of the ribbons.