A long-standing problem in geodynamics is how to incorporate surface plates in numerical models of mantle convection. Plates have usually rafts [1-3]. as a separate rheological layer [4,5] or as a high-viscosity region within weak zones [6-11]. Plates have also been generated intrinsically through the use of a more complex (non-newtonian) rheology for the entire model [12,13] but with a prescribed mantle flow. However, previous attempts to generate plates intrinsically and in a self-consistent manner (without prescribed flow) have not produced surface motions that appear plate-like [14-16]. Here we present a three-dimensional convection model that generates plates in a self-consistent manner through the use of rheology that is temperature and strain-rate dependent, and which incorporates the concept of a yield stress. This rheology induces a stiff layer on top of a convecting fluid, and we find that this layer breaks at sufficiently high stresses. The model produces a style of convection that contains some of the important features of plate tectonics, such as the subduction of the stiff layer and plate-like motion on the surface of the fluid mantle. However, the model also produces some non-Earth-like features, such as episodic subduction followed by the slow growth of a new stiff layer, which may be more consistent with the style of convection found on Venus.