We report a measurement of the rate of prompt diphoton production in pp collisions at s√=1.96  TeV using a data sample of 207  pb−1 collected with the upgraded Collider Detector at Fermilab. The background from nonprompt sources is determined using a statistical method based on differences in the electromagnetic showers. The cross section is measured as a function of the diphoton mass, the transverse momentum of the diphoton system, and the azimuthal angle between the two photons and is found to be consistent with perturbative QCD predictions