The authors studied the conduction mechanism in an uranium doped low dimensional magnetic system $Ca_2CuO_3$. This system exhibits the S=1/2 quasi 1D antiferromagnetic chains of -Cu-O- with strong magnetic coupling, and demonstrates continuous semiconductor-like behavior with constant covalent insulator character. This paper identifies the conduction is due to thermally activated phonon-assisted electron hopping between dopant uranium sites. The parameter a, the characteristic for hopping probability, was determined to be 0.18 ${AA}^{-1}$. This value manifests a relatively stronger hopping probability for $Ca_2CuO_3$ as compared with other uranium doped ceramics.