  We show how to define Chern-Simons matter theories with boundary. Rather than
imposing boundary conditions, we introduce new boundary degrees of freedom from
the beginning and show how they can be used to cancel the gauge non-invariance
of the Chern-Simons action. We apply this method to the ABJM theory with
boundary. By imposing also boundary conformal invariance, we determine the
required boundary action. This result allows us to derive the action for the
multiple self-dual strings living on M5-branes.
