We study a model of two self-avoiding walks that are allowed to cross. An attractive energy is associated with each crossing. We present a number of exact results on the free energy of this model and show the existence of a zipping temperature, below which the number of crossings becomes macroscopic. We give heuristic arguments which show that in d 2 and d 3 this zipping transition occurs at infinite temperature. Exact enumeration and Monte Carlo simulations on the square lattice strongly support this conjecture and lead to a precise value for the crossover exponent.