Strain-promoted azide–alkyne cycloaddition (SPAAC) reactions between azides and strained alkynes are some of the most widely used bioorthogonal reactions for molecular imaging applications, such as in positron emission tomography (PET). Radiolabeled azides and alkynes have been developed for click reactions; however, very few compounds have been studied in the intracellular space, where stability, selectivity, and reactivity may be affected by the surrounding complex intracellular environment. Motivated by the lack of tools to evaluate azide tracer candidates for bioorthogonal click reactions in the intracellular compartment, we designed and synthesized Hoechst-DBCO, a Hoechst 33258 derivative that accumulates in cells. Hoechst 33258 has strong DNA binding properties and is used as a courier to deliver dibenzocyclooctyne (DBCO), a strained alkyne, into the nucleus to track click reactions in living cells. The ultimate aim of this study was to develop an in vitro assay to detect and investigate specific SPAAC bioorthogonal click reactions in living cells and to evaluate permeability, uptake, and reactivity in the intracellular compartment. The Hoechst-DBCO compound we developed can help accelerate the evaluation of candidates for bioorthogonal click reactions and find suitable radiopharmaceuticals for imaging procedures.