Extensive 63Cu NMR measurements have been carried out on a magnetically aligned sample of the triple-layered superconductor Tl2Ba2Ca2Cu3O10-δ (Tc = 125 K). The 63Cu shifts in the three Cu-O layers all have a similar temperature dependence to that of 17O, showing that they probe the same static spin susceptibility. The magnetic properties of this material were found to resemble those of underdoped YBa2Cu3O7-δ. The Knight shift decreases dramatically with decreasing temperature below 150 K in the normal state, whereas the nuclear spin lattice relaxation rate (1/T1T) shows a broad maximum at approx. 165 K, indicating an opening of a spin gap well above Tc.