  We present an action for a six-dimensional superconformal field theory
containing a non-abelian tensor multiplet. All of the ingredients of this
action have been available in the literature. We bring these pieces together by
choosing the string Lie 2-algebra as a gauge structure, which we motivated in
previous work. The kinematical data contains a connection on a categorified
principal bundle, which is the appropriate mathematical description of the
parallel transport of self-dual strings. Our action can be written down for
each of the simply laced Dynkin diagrams, and each case reduces to a
four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie
algebra. Our action also reduces nicely to an M2-brane model which is a
deformation of the ABJM model. While this action is certainly not the desired
M5-brane model, we regard it as a key stepping stone towards a potential
construction of the (2,0)-theory.
