The nucleus Lu-163 has been populated through the fusion-evaporation reacti
on La-139(Si-29,5n)Lu-163 with a beam energy of 152 MeV. The electromagneti
c properties of several connecting transitions between two presumably triax
ial, 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 align
ed particle is coupled to a strongly deformed triaxial rotor. The wobbling
mode is uniquely related to triaxiality in nuclei.