Fractals are found in nature and play important roles in biological functions. However, it is challenging to controllably prepare biomolecule fractals. In this study, a series of Sierpiński triangles with global organizational chirality is successfully constructed by the coassembly of l-tryptophan and 1,3-bi(4-pyridyl)benzene molecules on Ag(111). The chirality is switched when replacing l-tryptophan by d-tryptophan. The fractal structures are characterized by low-temperature scanning tunneling microscopy at the single-molecule level. Density functional theory calculations reveal that intermolecular hydrogen bonds stabilize the Sierpiński triangles.