DNA built from modular repeats presents a challenge for gene synthesis. We present a solid surface-based sequential ligation approach, which we refer to as iterative capped assembly (ICA), that adds DNA repeat monomers individually to a growing chain while using hairpin 'capping' oligonucleotides to block incompletely extended chains, greatly increasing the frequency of full-length final products. Applying ICA to a model problem, construction of custom transcription activator-like effector nucleases (TALENs) for genome engineering, we demonstrate efficient synthesis of TALE DNA-binding domains up to 21 monomers long and their ligation into a nuclease-carrying backbone vector all within 3 h. We used ICA to synthesize 20 TALENs of varying DNA target site length and tested their ability to stimulate gene editing by a donor oligonucleotide in human cells. All the TALENS show activity, with the ones >15 monomers long tending to work best. Since ICA builds full-length constructs from individual monomers rather than large exhaustive libraries of pre-fabricated oligomers, it will be trivial to incorporate future modified TALE monomers with improved or expanded function or to synthesize other types of repeat-modular DNA where the diversity of possible monomers makes exhaustive oligomer libraries impractical.