Below T-N similar to 17 K the Si-29 NMR line in URu2Si2 exhibits a previous
ly unobserved field-independent nearly isotropic contribution to the Linewi
dth, which increases to similar to 12 G as T --> 0. We argue that this feat
ure does not arise from static freezing of the U-spin magnetization, but is
due to coupling between Si-29 spins and a hidden order parameter. We discu
ss time-reversal symmetry-breaking orbital antiferromagnetism and indirect
nuclear spin-spin interactions as possible coupling mechanisms. Further NMR
experiments and theoretical calculations are suggested.