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We define a 3-loop group $\Omega^3G$ as a subgroup of smooth maps from a3-ball to a Lie group $G$, and then construct a 2-group based on an automorphicaction on the Mickelsson-Faddeev extension of $\Omega^3G$. In this we followthe strategy of Murray et al., who earlier described a similar construction inone dimension. The three-dimensional situation presented here is furthercomplicated by the fact that the 3-loop group extension is not central.

A 2-group construction from an extension of the 3-loop group $\Omega^3G$