The physicochemical properties of nucleic acids are dominated by their highly charged phosphodiester backbone chemistry. This polyelectrolyte structure decouples information content (base sequence) from bulk properties, such as solubility, and has been proposed as a defining trait of all informational polymers. However, this conjecture has not been tested experimentally. Here, we describe the encoded synthesis of a genetic polymer with an uncharged backbone chemistry: alkyl phosphonate nucleic acids (phNAs) in which the canonical, negatively charged phosphodiester is replaced by an uncharged P-alkyl phosphonodiester backbone. Using synthetic chemistry and polymerase engineering, we describe the enzymatic, DNA-templated synthesis of P-methyl and P-ethyl phNAs, and the directed evolution of specific streptavidin-binding phNA aptamer ligands directly from random-sequence mixed P-methyl/P-ethyl phNA repertoires. Our results establish an example of the DNA-templated enzymatic synthesis and evolution of an uncharged genetic polymer and provide a foundational methodology for their exploration as a source of novel functional molecules.