Who was the chief god of the Babylonian pantheon?

The chief god of the Babylonian pantheon was Marduk.

Marduk began as the patron deity of Babylon and gradually rose as Babylon became the dominant political power in southern Mesopotamia. His elevation was expressed most dramatically in the Enūma Eliš, the Babylonian creation epic, where he defeats the sea goddess Tiamat and receives authority over the other gods. He was worshipped at the Esagila temple in Babylon.

Marduk's role extended beyond kingship. He was associated with creation, justice, water, agriculture, magic, medicine, and the planet Jupiter. Babylonian rulers presented their authority as granted by him, especially during the first millennium BCE, when royal inscriptions regularly called him king of the gods.

Ashur was the national god of Assyria, not Babylon. Enlil had been an older Mesopotamian authority and remained important in some traditions, while Anu was the ancient sky god. The exact hierarchy changed across centuries, but for the Babylonian pantheon in its mature form, Marduk is the canonical answer.