  We show in this paper that Abelian Chern-Simons term is induced in 2+1 and
3+1 dimensional rotating superfluid $^{3}$He-A and plays important roles in its
dynamics. Because U(1) symmetry is spontaneously broken in $^{3}$He-A,
Goldstone mode appears and contributes to induced Chern-Simons term. We found
that the coefficient of Chern-Simons term, which is equivalent to Hall
conductance, depends on an infra-red cut off of the Goldstone mode, and that
the orbital angular momentum of $^{3}$He-A in a cylinder geometry is derived
from Chern-Simons term.
