We report measurements of the charm–anticharm production asymmetries for Λc+, Σc++, Σc0, Σc++∗, Σc0∗, and Λc+(2625) baryons from the Fermilab photoproduction experiment FOCUS (E831). These asymmetries are integrated over the region where the spectrometer has good acceptance. In addition, we have obtained results for the photoproduction asymmetries of the Λc baryons as functions of pL, pT2, and xF. The integrated asymmetry for Λc+ production, (σΛc+−σΛc−)/(σΛc++σΛc−), is 0.111±0.018±0.012, significantly different from zero. The asymmetries of the excited states are consistent with the Λc asymmetry
