We have measured the total cross sections of Ω− and Ω¯+ forward (xF>~0) inclusive production in KL0-carbon interactions in the range EK0=80 to 280 GeV to be 3.5±1.4 and 2.4±1.0 μb, respectively. We observe that the xF distributions for both of these states are increasing from xF=0 to xF≈0.6. The p⊥2 distributions are described as an exponential function in p⊥ with an average p⊥2 of 0.540 GeV2/c2.