We report on the results of the first measurement of exclusive f_{0}(980) meson photoproduction on protons for E_{gamma}=3.0-3.8 GeV and -t=0.4-1.0 GeV2. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the pi;{+}pi;{-} channel by performing a partial wave analysis of the reaction gammap-->ppi;{+}pi;{-}. Clear evidence of the f_{0}(980) meson was found in the interference between P and S waves at M_{pi;{+}pi;{-}} approximately 1 GeV. The S-wave differential cross section integrated in the mass range of the f_{0}(980) was found to be a factor of about 50 smaller than the cross section for the rho meson. This is the first time the f_{0}(980) meson has been measured in a photoproduction experiment.