We have employed high-level coupled cluster methods including connected triple excitations to study the possibility of symmetry-breaking in the ²B₂ ground state of the c-C₃C₂H radical. Specifically, we find that spin-restricted open-shell Hartree–Fock (ROHF) reference orbitals yield a C_2v structure, whereas spin-unrestricted Hartree–Fock (UHF) and Brueckner orbitals lead to a symmetry-broken C_s minimum-energy geometry. Equation-of-motion coupled cluster singles and doubles method for ionized states yields a C_s structure with a double-zeta basis set, but not with a triple-zeta basis set. Through a detailed analysis of the orbital instability/near-instability behavior of each type of Hartree–Fock reference, we have determined that the UHF reference wave function is more reliable than the ROHF reference in this case and that the Born–Oppenheimer potential surface for c-C₃C₂H exhibits a symmetry broken C_s global minimum. This result is supported by excited-state computations, which indicate that a second-order (pseudo) Jahn–Teller interaction is responsible for the symmetry-breaking.