A detailed structural model for the indium-induced Si(111)-(4 x 1) surface reconstruction has been determined by analyzing an extensive set of x-ray-diffraction data recorded with monochromatic (h omega=9.1 keV) synchrotron radiation. The reconstruction is quasi-one-dimensional. The main features in the structure are chains of silicon atoms alternating with zigzag chains of indium atoms on top of an essentially unperturbed silicon lattice. The indium coverage corresponds to one monolayer. The structural model consistently explains all previously published experimental data.