Beagle Channel Arbitration

On 22 July 1971 Salvador Allende and Alejandro Lanusse, the Presidents of Chile and Argentina, signed an arbitration agreement (the Arbitration Agreement of 1971). This agreement related to their dispute over the territorial and maritime boundaries between them, and in particular the title to the Picton, Nueva and Lennox islands near the extreme end of the American continent, which was submitted to binding arbitration under the auspices of Queen Elizabeth II of the United Kingdom.

On 2 May 1977 the court ruled that the islands belonged to Chile (see the Report and decision of the Court of Arbitration). On 25 January 1978 Argentina repudiated the arbitration decision and on 22 December 1978 started (and a few hours later aborted) military action to invade both those islands and continental Chile.

The British Crown had previously in 1902 and 1966 acted as arbitrator between Chile and Argentina (see Arbitration 1902 here), but, given the growing Falkland Islands sovereignty dispute between Argentina and the United Kingdom, the parties agreed to change the statutory framework of the Arbitration.

The Arbitration Agreement of 1971 stipulated:

In this way the United Kingdom did not have any influence on the judgement: the procedure, the legal framework, the judges and the matter in dispute had all been defined by both countries.

The procedure had four phases:

...
Wikipedia