Abstract: Embodiments of a method for covalently immobilizing one or more discrete molecules on a substrate and embodiments of substrates having covalently-immobilized discrete molecules are disclosed. Embodiments of the method can include exposing a substrate to a functionalizing reagent to form a functionalized substrate and exposing the functionalized substrate to a solution comprising the molecule to be immobilized. A reaction-energy source then can be used to activate the functionalizing reagent and covalently bond one or more of the molecules to the substrate. All or a substantial portion of the unbonded molecules then can be removed. Controlling the concentration of the functionalizing reagent to which the substrate is exposed allows the density of the bonding sites on the substrate to be reduced so that, after removal of the unbonded molecules, at least one of the bonded molecules remains on the substrate spatially isolated from any other bonded molecules.