We report on the first experimental realization of a high-reflectivity cavity mirror that solely consists of a single silicon crystal. Since no material was added to the crystal, the urgent problem of "coating thermal noise" that currently limits classical as well as quantum measurements is avoided. Our mirror is based on a surface nanostructure that creates a resonant surface waveguide. In full agreement with a rigorous model we realized a reflectivity of (99.79+/-0.01)% at a wavelength of 1.55 microm, and achieved a cavity finesse of 2784. We anticipate that our achievement will open the avenue to next generation high-precision experiments targeting fundamental questions of physics.