We present a low-temperature scanning tunneling microscopy (STM) study on the supramolecular ordering of tetrapyridyl-porphyrin (TPyP) molecules on Ag(111). Vapor deposition in a wide substrate temperature range reveals that TPyP molecules easily diffuse and self-assemble into large, highly ordered chiral domains. We identify two mirror-symmetric unit cells, each containing two differently oriented molecules. From an analysis of the respective arrangement it is concluded that lateral intermolecular interactions control the packing of the layer, while its orientation is induced by the coupling to the substrate. This finding is corroborated by molecular mechanics calculations. High-resolution STM images recorded at 15 K allow a direct identification of intramolecular features. This makes it possible to determine the molecular conformation of TPyP on Ag(111). The pyridyl groups are alternately rotated out of the porphyrin plane by an angle of 60 degrees.