  A measurement of the spin of the Omega^- hyperon produced through the
exclusive process Xi_c^0 --> Omega^- K^+ is presented using a total integrated
luminosity of 116 fb^-1 recorded with the BABAR detector at the e^+ e^-
asymmetric-energy B-Factory at SLAC. Under the assumption that the Xi_c^0 has
spin 1/2, the angular distribution of the Lambda from Omega^- --> Lambda K^-
decay is inconsistent with all half-integer Omega^- spin values other than 3/2.
Lower statistics data for the process Omega_c^0 --> Omega^- pi^+ from a 230
fb^-1 sample are also found to be consistent with Omega^- spin 3/2. If the
Xi_c^0 spin were 3/2, an Omega^- spin of 5/2 cannot be excluded.
