An important development in recent synthesis strategies is the formation of electronically coupled one and two-dimensional organic systems for potential applications in nanoscale molecule-based devices. Here, we assemble one-dimensional spin chains by covalently linking basic molecular building blocks on a Au(111) surface. Their structural properties are studied by scanning tunneling microscopy and the Kondo effect of the basic molecular blocks inside the chains is probed by scanning tunneling spectroscopy. Tunneling spectroscopic images reveal the existence of separate Kondo regions within the chains while density functional theory calculations unveil antiferromagnetic coupling between the spin centers.