[en] The energy of the lowest deformed 2-particle 2-hole (2p2h) 0⁺ state in even-even N = 20 nuclei is a key observable directly related to the size of the neutron N = 20 shell closure. ³⁴Si, with 14 protons and 20 neutrons, lies at the boundary of the ⁱsland of inversion^, where the deformed 2p2h 0⁺ state is the ground state in even-A nuclei. In ³⁴Si, the 2p2h 0⁺ state is expected to be particularly low lying - in some theories it is even predicted to lie below the first 2⁺ state. While there have been a number of attempts, using various techniques, no experiment to date has been able to firmly locate the ³⁴Si 2p2h 0⁺ state although a number of candidates have been suggested. Here we present, for the first time, data obtained from a fusion-evaporation reaction ¹⁸O(¹⁸O, 2p) to produce ³⁴Si. Gammasphere and Microball were used to detect γ-γ coincidences and charged particles (two protons), respectively. The increased sensitivity of this experiment using γ-γ coincidences and a high charged-particle detection efficiency helped to exclude previously reported candidates and provided a stringent limit on the anticipated γ decay from the first 2⁺ state to the 2p2h 0⁺ state.