DNA–DNA cross‐linking agents constitute an important family of chemotherapeutics that non‐specifically react with endogenous nucleophiles and therefore exhibit undesirable side effects. Here we report a cationic Sondheimer diyne derivative “DiMOC” that exhibits weak, reversible intercalation into duplex DNA (Kd=15 μm) where it undergoes tandem strain‐promoted cross‐linking of azide‐containing DNA to give DNA‐DNA interstrand crosslinks (ICLs) with an exceptionally high apparent rate constant kapp=2.1×105 m−1 s−1. This represents a 21 000‐fold rate enhancement as compared the reaction between DIMOC and 5‐(azidomethyl)‐2′‐deoxyuridine (AmdU) nucleoside. As single agents, 5′‐bispivaloyloxymethyl (POM)‐AmdU and DiMOC exhibited low cytotoxicity, but highly toxic DNA‐DNA ICLs were generated by metabolic incorporation of AmdU groups into cellular DNA, followed by treatment of the cells with DiMOC. These results provide the first examples of intercalation‐enhanced bioorthogonal chemical reactions on DNA, and furthermore, the first strain‐promoted double click (SPDC) reactions inside of living cells.