Strange baryon pair production in two-photon collisions is studied with the L3 detector at LEP. The analysis is based on data collected at e+e− centre-of-mass energies from 91 GeV to 208 GeV, corresponding to an integrated luminosity of 844 pb−1. The processes γγ→ΛΛ and γγ→Σ0Σ0are identified. Their cross sections as a function of the γγ centre-of-mass energy are measured and results are compared to predictions of the quark–diquark model.