We report on the results of the first measurement of exclusive f0(980) meson photoproduction on protons for Eγ=3.0-3.8GeV and -t=0.4-1.0GeV2. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the π+π- channel by performing a partial wave analysis of the reaction γp→pπ+π-. Clear evidence of the f0(980) meson was found in the interference between P and S waves at Mπ+π-∼1GeV. The S-wave differential cross section integrated in the mass range of the f0(980) was found to be a factor of about 50 smaller than the cross section for the ρ meson. This is the first time the f0(980) meson has been measured in a photoproduction experiment.