We demonstrate the kinetically controlled growth of one-dimensional Co nanomagnets with a high lateral order on a nanopatterned Ag(110) surface. First, self-organized Si nanoribbons are formed upon submonolayer condensation of Si on the anisotropic Ag(110) surface. Depending on the growth temperature, individual or regular arrays (with a pitch of 2 nm) of Si nanoribbons can be grown. Next, the Si/Ag(110) system is used as a novel one-dimensional Si template to guide the growth of Co dimer nanolines on top of the Si nanoribbons, taking advantage of the fact that the thermally activated process of Co diffusion into the Si layer is efficiently hindered at 220 K. Magnetic characterization of the Co nanolines using X-ray magnetic circular dichroism reveals that the first atomic Co layer directly adsorbed onto the Si nanoribbons presents a weak magnetic response. However, the second Co layer exhibits an enhanced magnetization, strongly suggesting a ferromagnetic ordering with an in-plane easy axis of magnetization, which is perpendicular to the Co nanolines.