Final answer:
Pelops is the member of the House of Atreus depicted on the Temple of Zeus at Olympia, swearing an oath before his chariot race against Oenomaus as part of the temple's sculptural program.
Step-by-step explanation:
The member of the House of Atreus depicted on the Temple of Zeus at Olympia, swearing an oath before a chariot race against Oenomaus, is Pelops. This scene is part of a much larger sculptural program of the temple, which includes various other mythological scenes, such as the Twelve Labors of Herakles and the Centauromachy. The East Pediment of the Temple of Zeus showcased this particular myth, where Pelops sought to win the hand of Hippodameia, the daughter of Oenomaus, through a chariot race, promising to honor the gods if he won. This oath, and the chariot race, are fundamental elements of Pelops' story and provide a rich narrative for the decoration of the temple which was constructed around 470-456 BCE.