Adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) approaches are developed for the first time. A new phenomenon, the existence of multiple chiral doublets (M{chi}D), i.e., more than one pair of chiral doublet bands in one single nucleus, is suggested for {sup 106}Rh based on the triaxial deformations and their corresponding proton and neutron configurations.