  We analyze the nuclear magnetic relaxation rate $(1/T_1)_{orb}$ due to the
coupling of nuclear spin to the orbital moment of itinerant electrons in
metals. In the clean non--interacting case, contributions from large--distance
current fluctuations add up to cause a divergence of $(1/T_1)_{orb}$. When
impurity scattering is present, the elastic mean free time $\tau$ cuts off the
divergence, and the magnitude of the effect at low temperatures is controlled
by the parameter $\ln(\mu \tau)$, where $\mu$ is the chemical potential. The
spin--dipolar hyperfine coupling, while has the same spatial variation $1/r^3$
as the orbital hyperfine coupling, does not produce a divergence in the nuclear
magnetic relaxation rate.
