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Using scanning tunneling microscopy, we examine an uncommon aggregation of polyaromatic chiral molecules on a silver surface. Dense packing is achieved through a chiral triangular tiling of triads, with\n                    <jats:italic>N<\/jats:italic>\n                    and\n                    <jats:italic>N<\/jats:italic>\n                    \u2009\u00b1\u20091 molecules at the edges. The triangles feature a random distribution of mirror-isomers, with a significant excess of one isomer. Chirality at the domain boundaries causes a lateral shift, producing three distinct topological defects where six triangles converge. These defects partially contribute to the formation of supramolecular spirals. The observation of different equal-density arrangements suggests that entropy maximization must play a crucial role. Despite the potential for regular patterns, all observed tiling is aperiodic. Differences from previously reported aperiodic molecular assemblies, such as Penrose tiling, are discussed. 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