Here, the Li7(γ,t)He4 ground state cross section was measured for the first time using monoenergetic γ rays with energies between 4.4 and 10 MeV at the High Intensity Gamma-ray Source. The reaction is important for the primordial Li problem and for testing our understanding of the mirror α -capture reactions H 3(α,γ)Li7 and He3(α,γ)Be7 . Although over the last 30 years most measurements of the H 3(α,γ)Li7 reaction have concentrated in an energy range below Eγ=3.65 MeV, measurements at higher energies could potentially restrict the extrapolation to astrophysically important energies. The experimental arrangement for measuring the Li7(γ,t)He4 reaction included a large-area silicon detector array and several beam characterization instruments. The experimental astrophysical S factor of H 3(α,γ) calculated from the present data was fitted using the R -matrix formalism. The results are in disagreement with previous experimental measurements in the same energy range but the extrapolated S factor agrees with the potential model calculation and lower energy experimental data.