  Two distinct sets of chiral-partner bands have been identified in the nucleus
$^{133}$Ce. They constitute a multiple chiral doublet (M$\chi$D), a phenomenon
predicted by relativistic mean field (RMF) calculations and observed
experimentally here for the first time. The properties of these chiral bands
are in good agreement with results of calculations based on a combination of
the constrained triaxial RMF theory and the particle-rotor model.
