The nucleus (163)Lu has been populated through the fusion-evaporation reaction (139)La((29)Si,5n)(163)Lu with a beam energy of 152 MeV. The electromagnetic properties of several connecting transitions between two presumably triaxial, strongly deformed (TSD) bands have been studied. Evidence is presented for the assignment of the excited TSD band as a wobbling mode built on the yrast TSD band, based on comparisons to new calculations in which an aligned particle is coupled to a strongly deformed triaxial rotor. The wobbling mode is uniquely related to triaxiality in nuclei.