The He-3 longitudinal spin-relaxation rate T-1(-1) is crucial for productio
n of highly polarized He-3 by spin-exchange optical pumping. We show that T
-1(-1) is increased by a factor of 2-20 solely by exposure of spin-exchange
cells to a few-kG magnetic field. The original T-1(-1) can be restored by
degaussing the cell. The effect is attributed to magnetic surface sites and
has been observed in both Pyrex and aluminosilicate-glass cells. Our resul
ts both advance the understanding of wall relaxation and demonstrate the us
e of He-3 as an extremely sensitive probe of surface magnetism.