We investigated Pt-induced nanowires on the Si(110) surface using scanning tunneling microscopy (STM) and angle-resolved photoemission. High resolution STM images show a well-ordered nanowire array of 1.6 nm width and 2.7 nm separation. Angle-resolved photoemission reveals fully occupied one-dimensional (1D) bands with a Rashba-type split dispersion. Local dI/dV spectra further indicate well-confined 1D electron channels on the nanowires, whose density of states characteristics are consistent with the Rashba-type band splitting. The observed energy and momentum splitting of the bands are among the largest ever reported for Rashba systems, suggesting the Pt-Si nanowire as a unique 1D giant Rashba system. This self-assembled nanowire can be exploited for silicon-based spintronics devices as well as the quest for Majorana fermions.