The 02(+) state in 34Si has been populated at the GANIL-LISE3 facility through the β decay of a newly discovered 1(+) isomer in 34Al of 26(1) ms half-life. The simultaneous detection of e(+)e(-) pairs allowed the determination of the excitation energy E(02(+))=2719(3) keV and the half-life T(1/2)=19.4(7) ns, from which an electric monopole strength of ρ(2)(E0)=13.0(0.9)×10(-3) was deduced. The 2(1)(+) state is observed to decay both to the 0(1)(+) ground state and to the newly observed 0(2)(+) state [via a 607(2) keV transition] with a ratio R(2(1)(+)→0(1)(+)/2(1)(+)→0(2)(+))=1380(717). Gathering all information, a weak mixing with the 0(1)(+) and a large deformation parameter of β=0.29(4) are found for the 0(2)(+) state, in good agreement with shell model calculations using a new SDPF-U-MIX interaction allowing np-nh excitations across the N=20 shell gap.