This paper considers a biologically relevant question of a Gaussian chain (such as an unfolded protein) binding to a sequence of receptors with matching multiple ligands distributed along the chain. Using the characteristic time for a tethered ligand to bind to a surface receptor, we study the case of multiple binding to a linear sequence of receptors on the surface. The tethered binding time is determined by the entropic barrier for the chain to be stretched sufficiently to reach the distant receptor target, and a restriction on chain conformations near the substrate. Adsorption (multiple-site binding) is shown to be dominated by a simple zipper sequence, only occasionally accelerated by loop formation. However, when the number of receptors increases, a competing rate-limiting process takes over: the center of mass of the remaining free chain has to drift down the line of receptors, which takes longer when the receptors are close and the entropic pulling force is low. As a result, the time for the complete chain adsorption is minimised by a certain optimal number of receptors, depending on the distance to be traversed by the free end, and the chain length.