The mechanism of the reaction between acetylene and ozone to form a primary ozonide (POZ) in the gas phase has been studied theoretically. The concerted pathway, HCCH + O-3 -> POZ, proceeds via a biradicaloid transition state TS0. The stepwise pathway is a three-step reaction, HCCH + O-3 -> M1 -> M2 -> POZ, involving two biradical TSs and two biradical intermediates M1 and M2. The segment of the global potential energy surface (PES) for the concerted pathway is characterized as a R-PES, which is obtained from the restricted (R) density functional theory and Hartree-Fock-based methods. The RDFT and RHF solutions of TS0 and O-3 are unstable toward spin-symmetry breaking. The wave function instability for TS0 and O-3 results in a discontinuity between the R-PES and the region of the global PES encompassing the biradical TSs and the intermediates of the stepwise pathway, which are characterized with unrestricted (U) methods. The global PES is characterized separately as an U(R)-PES using a combination of the R and U methods. Several different values of barriers for the concerted pathway and the energy of concert (E-c) can be estimated due to complications arising from the discontinuity between the R- and the U(R)-PES and the existence of two different RDFT and UDFT O-3 equilibrium geometries. RCCSD(T)//RDFT predicts a barrier of 8.2 kcal/mol. U(R)CCSD(T)/U(R)DFT predicts a barrier of 13.8 kcal/mol for the concerted and 15.3 kcal/mol for the stepwise pathway. Comparison between the R-PES barrier to the concerted pathway and the U(R)-PES barrier to the stepwise pathway suggests the former to be the only significant mechanism. Consideration of the energy difference between TS1, the TS for the first step of the stepwise mechanism, and TS0 within the global PES leads to a significantly smaller E-c. Geometry optimization with CASSCF and energy point calculations with MRMP2 are employed to characterize TS0 and TS1. MRMP2//CASSCF predicts the energy level of TS1 to be higher than that of TS0 by 2 kcal/mol. Analysis of experimental and computational data based on the low estimate of E-c shows that the possibility of the stepwise pathway being a secondary channel at elevated temperatures cannot be ruled out.