Reconstructed ii baryon decays and photon conversions in DELPHI are us
ed to measure the Sigma(0) production rate from hadronic Z(0) decays a
t LEP. The number of Sigma(0) decays per hadronic Z decay is found to
be: <Sigma(0) + <(Sigma)over bar (0)>> = 0.070 +/- 0.010 (stat.) +/- 0
.010 (syst.). The Omega(-) production rate is similarly measured to be
: <Omega(-) + <(Omega)over bar (+)> = 0.0014 +/- 0.0002 (stat.) +/- 0.
0004 (syst.) by a combination of methods using constrained fits to the
whole decay chain and particle identification.