  Multiplicative bundle gerbes are gerbes over a Lie group which are compatible
with the group structure. In this article connections on such bundle gerbes are
introduced and studied. It is shown that multiplicative bundle gerbes with
connection furnish geometrical constructions of the following objects: smooth
central extensions of loop groups, Chern-Simons actions for arbitrary gauge
groups, and symmetric bi-branes for WZW models with topological defect lines.
