We have developed a method to grow large, self-assembled, defect-free arrays of vacancy or adatom stripes on atomically flat, boron-doped Si(001)-(2\ifmmode\times\else\texttimes\fi{}1). The subnanometer-high stripes form between \ensuremath{\sim}870 and 990 \ifmmode^\circ\else\textdegree\fi{}C, with a spacing that depends on temperature. Si deposition is used to prevent sublimation-induced defect formation and to allow time for ordering via surface diffusion. Ordering mechanisms, observed in real time by low-energy electron microscopy, include island nucleation and growth, longitudinal splitting, and coarsening. At formation temperatures, the arrays are only stable when the area fractions of vacancy (${\ensuremath{\theta}}_{\mathrm{v}}$) or adatom stripes (${\ensuremath{\theta}}_{\mathrm{a}}$) are \ensuremath{\sim}\textonehalf{}, consistent with stress domain theory predictions. At room temperature, arrays are preserved indefinitely and are a potential template for nanowire growth.