We study the spin fluctuation dynamics of Cu-O chains in the oxygen deficient planes of YBa₂Cu₃O_6+x. The chains are described by a model including antiferromagnetic interactions between the spins and Kondo-like scattering of the oxygen holes by the copper spins. There are incommensurate spin fluctuations along the direction of the chains. The dynamic structure factor of this system is qualitatively different from that of a quasi one-dimensional localized antiferromagnet due to the presence of itinerant holes. We compute the dynamic structure factor that could be measured in neutron scattering experiments.