A new chain structure of Au is found on stepped Si(111) which exhibits a 1/4-filled band and a pair of > or =1/2-filled bands with a combined filling of 4/3. Band dispersions and Fermi surfaces for Si(553)-Au are obtained by photoemission and compared to that of Si(557)-Au. The dimensionality of both systems is determined using a tight binding fit. The fractional band filling makes it possible to preserve metallicity in the presence of strong correlations.