Oligonucleotides are almost exclusively synthesized using the nucleoside phosphoramidite method, even though it is limited to the direct synthesis of approximately 200 mers and produces hazardous waste. Here, we describe an oligonucleotide synthesis strategy that uses the template-independent polymerase terminal deoxynucleotidyl transferase (TdT). Each TdT molecule is conjugated to a single deoxyribonucleoside triphosphate (dNTP) molecule that it can incorporate into a primer. After incorporation of the tethered dNTP, the 3′ end of the primer remains covalently bound to TdT and is inaccessible to other TdT-dNTP molecules. Cleaving the linkage between TdT and the incorporated nucleotide releases the primer and allows subsequent extension. We demonstrate that TdT-dNTP conjugates can quantitatively extend a primer by a single nucleotide in 10-20 s, and that the scheme can be iterated to write a defined sequence. This approach may form the basis of an enzymatic oligonucleotide synthesizer.