The government of Timor-Leste initiated this action under the United Nations Convention on the Law of the Sea.
The Sunrise gas development in the Timor Sea could be unlocked if there is a successful outcome in this long-standing dispute between the two governments.
Today's hearing will take place at the headquarters of the Permanent Court of Arbitration.
Timor-Leste's government spokesperson said last month the Conciliation Commission is chaired by Peter Taksoe-Jensen (of Denmark).