We examine the possibility that three hydrogen atoms in one plane of the cyclopropane dication come together in a concerted "ring-closing" mechanism to form H3+, a crucial cation in interstellar gas-phase chemistry. Ultrafast strong-field ionization followed by disruptive probing measurements indicates that the formation time of H3+ is 249 ± 16 fs. This time scale is not consistent with a concerted mechanism, but rather a process that is preceded by ring opening. Measurements on propene, an isomer of cyclopropane, reveal the H3+ formation time to be 225 ± 13 fs, a time scale similar to the H3+ formation time in cyclopropane. Ab initio molecular dynamics simulations and the fact that both dications share a common potential energy surface support the ring-opening mechanism. The reaction mechanism following double ionization of cyclopropane involves ring opening, then H-migration, and roaming of a neutral H2 molecule, which then abstracts a proton to form H3+. These results further our understanding of complex interstellar chemical reactions and gas-phase reaction dynamics relevant to electron ionization mass spectrometry.