  We provide a model of the String group as a central extension of
finite-dimensional 2-groups in the bicategory of Lie groupoids, left-principal
bibundles, and bibundle maps. This bicategory is a geometric incarnation of the
bicategory of smooth stacks and generalizes the more na\"ive 2-category of Lie
groupoids, smooth functors, and smooth natural transformations. In particular
this notion of smooth 2-group subsumes the notion of Lie 2-group introduced by
Baez-Lauda. More precisely we classify a large family of these central
extensions in terms of the topological group cohomology introduced by G. Segal,
and our String 2-group is a special case of such extensions. There is a nerve
construction which can be applied to these 2-groups to obtain a simplicial
manifold, allowing comparison with with the model of A. Henriques. The
geometric realization is an $A_\infty$-space, and in the case of our model, has
the correct homotopy type of String(n). Unlike all previous models our
construction takes place entirely within the framework of finite dimensional
manifolds and Lie groupoids. Moreover within this context our model is
characterized by a strong uniqueness result. It is a unique central extension
of Spin(n).
