The C amount and the structure of the Si(001)-c(4 x 4) surface is studied using scanning tunneling microscopy (STM) and ab initio calculations. The c(4 x 4) phase is found to contain 1/8 monolayer C (1 C atom in each primitive unit cell). From the C amount and the symmetry of high-resolution STM images, it is inferred that the C atoms substitute the fourth-layer site below the dimer row. We construct a structure model relying on ab initio energetics and STM simulations. Each C atom induces an on-site dimer vacancy and two adjacent rotated dimers on the same dimer row. The c(4 x 4) phase constitutes the subsurface Si(0.875)C(0.125) delta layer with two-dimensionally ordered C atoms.