  We present a variable temperature Scanning Tunneling Microscopy and
Spectroscopy (STM and STS) study of the Si(553)-Au atomic chain reconstruction.
This quasi one-dimensional (1D) system undergoes at least two charge density
wave (CDW) transitions at low temperature, which can be attributed to
electronic instabilities in the fractionally-filled 1D bands of the
high-symmetry phase. Upon cooling, Si(553)-Au first undergoes a single-band
Peierls distortion, resulting in period doubling along the imaged chains. This
Peierls state is ultimately overcome by a competing tripleperiod CDW, which in
turn is accompanied by a x2 periodicity in between the chains. These locked-in
periodicities indicate small charge transfer between the nearly half-filled and
quarter-filled 1D bands. The presence and the mobility of atomic scale
dislocations in the x3 CDW state indicates the possibility of manipulating
phase solitons carrying a (spin,charge) of (1/2,+-e/3) or (0,+-2e/3).
