We report on measurements of the inclusive production rate of Σ+ and Σ0 baryons in hadronic Z decays collected with the L3 detector at LEP. The Σ+ baryons are detected through the decay Σ+→pπ0, while the Σ0 baryons are detected via the decay mode Σ0→Λγ. The average numbers of Σ+ and Σ0 per hadronic Z decay are measured to be: (NΣ+)+(NΣ-)=0.114±0.011stat.±0.009syst.; (NΣ0)+(NΣ0)=0.095±0.015stat.±0.013syst. These rates are found to be higher than the predictions from Monte Carlo hadronization models and analytical parameterizations of strange baryon production.