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 $\gamma \gamma \rightarrow \Lambda \overline{\Lambda}$ and $\gamma \gamma \rightarrow \Sigma^0 \overline{\Sigma}\,\!^0$ are identified. Their cross sections as a function of the $\gamma \gamma$ centre-of-mass energy are measured and results are compared to predictions of the quark-diquark model.