Recently, high-resolution Chandra observations revealed the existence of very sharp features in the X-ray surface brightness and temperature maps of several clusters. These features, called cold fronts, are characterized by an increase in surface brightness by a factor 2 over 10-50 kpc accompanied by a drop in temperature of a similar magnitude. The existence of such sharp gradients can be used to put interesting constraints on the physics of the intracluster medium (ICM) if their mechanism and longevity are well understood. Here, we present results of a search for cold fronts in high-resolution simulations of galaxy clusters in cold dark matter models. We show that sharp gradients with properties similar to those of observed cold fronts naturally arise in cluster mergers when the shocks heat gas surrounding the merging subcluster, while its dense core remains relatively cold. The compression induced by supersonic motions and shock heating during the merger enhance the amplitude of gas density and temperature gradients across the front. Our results indicate that cold fronts are nonequilibrium transient phenomena and can be observed for a period of less than a billion years. We show that the velocity and density fields of gas surrounding the cold front can be very irregular, which would complicate analyses aiming to put constraints on the physical conditions of the ICM in the vicinity of the front.