It said the decision following the hearing, which was held on May 13 and 14, would be likely to take weeks or months and there is no fixed date.
The tribunal was dealing with the challenge from the Republic that the tribunal does not actually have jurisdiction to hear the group's claim for compensation.
As reported in March this year, the arbitration cases for Churchill and its subsidiary, Planet, have been consolidated into a single proceeding and will be heard together.
They are seeking compensation from the Republic after the expropriation of the firm's rights over the huge East Kutai coal mine in Indonesia.
Churchill and Planet were represented by the international law firm Quinn Emanuel Urquhart & Sullivan, LLP.