There is a unique transition element "g"ρστ in Γ"i" such that "g""ρστ"·"ψ"" = "ψ"·"ψ"′. The relations satisfied by the transition elements of an orbifold imply those required for a complex of groups. In this way a complex of groups can be canonically associated to the nerve of an open covering by orbifold (or orbispace) charts. In the language of non-commutative sheaf theory and gerbes, the complex of groups in this case arises as a sheaf of groups associated to the covering "U""i"; the data "g"ρστ is a 2-cocycle in non-commutative sheaf cohomology and the data "h"στ gives a 2-coboundary perturbation.