  We construct an effective action describing an elementary M5-brane
interacting with dynamical eleven-dimensional supergravity, which is free from
gravitational anomalies. The current associated to the elementary brane is
taken as a distribution valued delta-function on the support of the 5-brane
itself. Crucial ingredients of the construction are the consistent inclusion of
the dynamics of the chiral two-form on the 5-brane, and the use of an invariant
Chern-kernel allowing to introduce a D=11 three-form potential which is well
defined on the worldvolume of the 5-brane.
