The design and synthesis of protein-like polymers is a fundamental challenge in materials science. A means to achieve this goal is to create synthetic polymers of defined sequence where all relevant folding information is incorporated into a single polymer strand. We present here the aqueous self-assembly of peptoid polymers (N-substituted glycines) into ultrathin, two-dimensional highly ordered nanosheets, where all folding information is encoded into a single chain. The sequence designs enforce a two-fold amphiphilic periodicity. Two sequences were considered: one with charged residues alternately positive and negative (alternating patterning), and one with charges segregated in positive and negative halves of the molecule (block patterning). Sheets form between pH 5 and 10 with the optimal conditions being pH 6 for the alternating sequence and pH 8 for the block sequence. Once assembled, the nanosheets remain stable between pH 6 and 10 with observed degradation beginning to occur below pH 6. The alternating charge nanosheets remain stable up to concentrations of 20% acetonitrile, whereas the block pattern displayed greater robustness remaining stable up to 30% acetonitrile. These observations are consistent with expectations based on considerations of the molecules' electrostatic interactions. This study represents an important step in the construction of abiotic materials founded on biological informatic and folding principles.