Total and differential cross sections for exclusive production of proton-antiproton pairs in photon-photon collisions have been measured using the JADE detector at PETRA. The total cross section in the CM angular |cos θ∗| < 0.6 reaches a maximum value of 3.8 nb for a γγ invariant mass of Wγγ = 2.25 GeV, and decreases rapidly for higher values of Wγγ. In the range 2.0 GeV < Wγγ < 2.6 GeV the angular distribution is not isotopic. The nucleons are preferentially emitted at large angles to the collision axis.