Two-dimensional covalent organic frameworks (2D COFs) are layered, structurally regular, and permanently porous macromolecules. When reactive groups are embedded into a COF structure, subsequent chemical reactions can be performed following polymerization. As such, a postsynthetic modification (PSM) strategy provides diverse materials from a single set of COF monomers and polymerization protocols. Here, we report the synthesis of an asymmetric dibenzocyclooctyne-containing iminelinked 2D COF, which readily undergoes strain-promoted azide-alkyne cycloaddition (SPAAC) reactions without catalyst under mild and dilute conditions. This approach was used to quantitatively decorate the COF lattice with alkyl chains and amines, all without the need for exogenous species. Functionalization may result in spontaneous delamination of bulk COF materials into solution-stable sheets, demonstrating the utility of this technique. As such, this platform is useful for postsynthetic functionalization with sensitive chemical functionalities that are not amenable to direct polymerization or existing PSM strategies.