Chemotaxis provides a mechanism for directing the transport of molecules along chemical gradients. Here, we show the chemotactic migration of dye molecules in response to the gradients of several different neutral polymers. The magnitude of chemotactic response depends on the structure of the monomer, polymer molecular weight and concentration, and the nature of the solvent. The mechanism involves cross diffusion up the polymer gradient, driven by favorable dye polymer interaction. Modeling allows us to quantitatively evaluate the strength of the interaction and the effect of the various parameters that govern chemotaxis.