  From a certain strongly equivariant bundle gerbe with connection and curving
over a smooth manifold on which a Lie group acts, we construct under some
conditions a bundle gerbe with connection and curving over the quotient space.
In general, the construction requires a choice, and we can consequently obtain
distinct stable isomorphism classes of bundle gerbes with connection and
curving over the quotient space. A bundle gerbe naturally arising in
Chern-Simons theory provides an example of the reduction.
