Production of chemical concentration gradients on the submicrometer scale remains a formidable challenge, despite the broad range of potential applications and their ubiquity throughout nature. We present a strategy to quantitatively prescribe spatial variations in functional group concentration using ThermoChemical NanoLithography (TCNL). The approach uses a heated cantilever to drive a localized nanoscale chemical reaction at an interface, where a reactant is transformed into a product. We show using friction, force microscopy that localized gradients in the product concentration have a spatial resolution of similar to 20 nm where the entire concentration profile is confined to sub-180 nm. To gain quantitative control over the concentration, we introduce a chemical kinetics model of the thermally driven nanoreaction that shows excellent agreement with experiments. The comparison provides a calibration of the nonlinear dependence of product concentration versus temperature, which we use to design two-dimensional temperature maps encoding the prescription for linear and nonlinear gradients. The resultant chemical nanopatterns show high fidelity to the user-defined patterns, including the ability to realize complex chemical patterns with arbitrary variations in peak concentration with a spatial resolution of 180 nm or better. While this work focuses on producing chemical gradients of amine groups, other functionalities are a straightforward modification. We envision that using the basic scheme introduced here, quantitative TCNL will be capable of patterning gradients of other exploitable physical or chemical properties such as fluorescence in conjugated polymers and conductivity in graphene. The access to submicrometer chemical concentration and gradient patterning provides a new dimension of control for nanolithography.