The growth of Au on the Si(001) surface is studied using scanning tunneling microscopy (STM). We investigate the initial stages of Au overlayer formation on the Si surface at room temperature. Au grows on the substrate in a layer-by-layer fashion for Au coverage up to 3 monolayers. In the first layer growth, Au forms two-dimensional islands of local 2X2 structure with a density of one Au atom per Si surface atom. On the basis of the STM images, a 2X2 structural model is proposed. Au atoms lie in atop sites, forming Au-Au dimers with orientation perpendicular to the underlying Si dimers. Subsequent layers of Au growth are disordered.