A stable high-index surface of silicon, Si(5 5 12), is described. This surface forms a 2 x 1 reconstruction with one of the largest unit cells ever observed, 7.7 angstroms by 53.5 angstroms. Scanning tunneling microscopy (STM) reveals that the 68 surface atoms per 2 x 1 unit cell are reconstructed only on a local scale. A complete structural model for the surface is proposed, incorporating a variety of features known to exist on other stable silicon surfaces. Simulated STM images based on this model have been computed by first-principles electronic-structure methods and show excellent agreement with experiment.