  We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory. Its
symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant
non singular bilinear form. We analyze the gauge invariance of the theory and
show that action is invariant under a higher gauge transformation up to a
higher winding number. We find that the theory admits two seemingly
inequivalent canonical quantizations. The first is manifestly topological, it
does not require a choice of any additional structure on the spacial 3-fold.
The second, more akin to that of ordinary Chern-Simons theory, involves fixing
a CR structure on the latter. Correspondingly, we obtain two sets of semistrict
higher WZW Ward identities and we find the explicit expressions of two higher
versions of the WZW action. We speculate that the model could be used to define
2-knot invariants of 4-folds.
