We have limited a CPT-violating correlation in annihilations of polarized ortho-positronium. We searched for an asymmetry in the triple correlation s-->.(k-->(1)xk-->(2)), where k-->(1) and k-->(2) are the two largest photon momenta, and s--> is the spin of the positronium. Using the Gammasphere array of Compton-suppressed high-purity germanium detectors, we detected 2.65x10(7) events of ortho-Ps annihilation. The amplitude of a CPT-violating asymmetry in the data set is found to be 0.0026+/-0.0031, a factor of 6 smaller than previous experiments.