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: \begin{eqnarray*} \left N_{\Sigma^+} \right + \left N_{\bar{\Sigma}^+} \right & = & 0.114 \pm 0.011_{\mbox{\it \small stat}} \pm 0.009_{\mbox{\it \small syst}} \\ \left N_{\Sigma^0} \right + \left N_{\bar{\Sigma}^0} \right & = & 0.095 \pm 0.015_{\mbox{\it \small stat}} \pm 0.013_{\mbox{\it \small syst}} \ \mbox{.} \end{eqnarray*} These rates are found to be higher than the predictions from Monte Carlo hadronization models and analytical parameterizations of strange baryon production