In the context of the standard model of particle physics, there is a definite upper limit to the density of stable compact stars. However, if a more fundamental level of elementary particles exists, in the form of preons, stability may be re-established beyond this limiting density. We show that a degenerate gas of interacting fermionic preons does allow for stable compact stars, with densities far beyond that in neutron stars and quark stars. In keeping with tradition, we call these objects "preon stars", even though they are small and light compared to white dwarfs and neutron stars. We briefly note the potential importance of preon stars in astrophysics, e.g., as a candidate for cold dark matter and sources of ultra-high energy cosmic rays, and a means for observing them.