The design and synthesis of protein-like polymers is a fundamental challenge in materials science. A biomimetic approach is to explore the impact of monomer sequence on non-natural polymer structure and function. We present the aqueous self-assembly of two peptoid polymers into extremely thin two-dimensional (2D) crystalline sheets directed by periodic amphiphilicity, electrostatic recognition and aromatic interactions. Peptoids are sequence-specific, oligo-N-substituted glycine polymers designed to mimic the structure and functionality of proteins. Mixing a 1: 1 ratio of two oppositely charged peptoid 36mers of a specific sequence in aqueous solution results in the formation of giant, free-floating sheets with only 2.7nm thickness. Direct visualization of aligned individual peptoid chains in the sheet structure was achieved using aberration-corrected transmission electron microscopy. Specific binding of a protein to ligand-functionalized sheets was also demonstrated. The synthetic flexibility and biocompatibility of peptoids provide a flexible and robust platform for integrating functionality into defined 2D nanostructures.