  We report measurements of the charm-anticharm production asymmetries for
$\Lambda_c^+$, $\Sigma_c^{++}$, $\Sigma_c^0$, $\Sigma_c^{++*}$,
$\Sigma_c^{0*}$, and $\Lambda_c^+(2625)$ 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 $\Lambda_c$ baryons
as functions of $p_L$, $p_T^2$, and $x_F$. The integrated asymmetry for
$\Lambda_c^+$ production, $(\sigma_{\Lambda_c^+} - \sigma_{\Lambda_c^-}) /
(\sigma_{\Lambda_c^+} + \sigma_{\Lambda_c^-})$, is $0.111 \pm 0.018 \pm 0.012$,
significantly different from zero. The asymmetries of the excited states are
consistent with the $\Lambda_c$ asymmetry.
