We introduce an algorithm for off-lattice kinetic Monte Carlo simulations of heteroepitaxial crystal growth. In heteroepitaxy a mismatch of the lattice constants in adsorbate and substrate can lead to a variety of phenomena already within the first monolayers of growth. This includes the appearance of misfit dislocations or the formation of self-assembled islands. In order to gain general insight into the relevant mechanisms we study, as a first example, a Lennard-Jones system in 1 + 1 dimensions. The critical layer thickness for the occurrence of dislocations is determined as a function of the misfit. Furthermore, we investigate the 2D-3D transition which marks the emergence of mounds from initially flat islands on the surface.