Question: What possession was Chile and Argentina disputing that led to Operation Soberania?

Context paragraphs:
Eladio Rojas: Eladio Alberto Rojas Díaz (8 November 1934, Tierra Amarilla, Chile – 13 January 1991, Viña del Mar, Chile) is a former Chilean footballer who played as a midfielder for Everton and Colo-Colo of Chile, River Plate of Argentina, and the Chile national football team in the 1962 FIFA World Cup on home soil.  Rojas scored the match winning goal for Chile in the 90th minute against Yugoslavia in the 1962 World Cup; his goal secured a third place finish for the World Cup hosts, which is Chile's best finish in the tournament to date.  Rojas was also a starter on the River Plate teams of the 1960s that fiercely contested the Argentine Primera División title.  While Rojas never won the title, River Plate did manage to place second in 1962 and 1963 as well as third in 1964.

Guillermo Rivera Aránguiz: Guillermo Andrés Rivera Aránguiz born 2 February 1989, in San Felipe, Chile) is a Chilean professional tennis player.  Rivera will be eligible to play in Davis Cup competitions for Chile in March 2011 against the United States.  He made his debut in Davis Cup singles for disputing the fifth point of the series against the United States, facing John Isner, losing him 3–6, 7–6, 5–7.

Papal mediation in the Beagle conflict: The Papal mediation in the Beagle conflict followed the failure of negotiations between Chile and Argentina, when, on 22 December 1978, the Argentinian Junta started Operation Soberanía, to invade Cape Horn and islands awarded to Chile by the Beagle Channel Arbitration.  Soon after the event, Pope John Paul II, offered to mediate and sent his personal envoy Cardinal Antonio Samoré to Buenos Aires.  Argentina, in acceptance of the authority of the Pope over the overwhelmingly Catholic Argentine population, called off the military operation and accepted the mediation.  On 9 January 1979 Chile and Argentina signed the Act of Montevideo formally requesting mediation by the Vatican and renouncing the use of force.

Beagle conflict: The Beagle conflict was a border dispute between Chile and Argentina over the possession of Picton, Lennox and Nueva islands and the scope of the maritime jurisdiction associated with those islands that brought the countries to the brink of war in 1978.

Chile national under-20 football team: Chile national U-20 football team, also known as Chile Sub-20 or La Rojita, is part of the Federación de Fútbol de Chile.  The U-20 team is considered to be the breeding ground for future Chile national soccer team players.  The Chile U-20 national team has participated in seven U-20 World Cups Chile 1987, Qatar 1995, Argentina 2001, Netherlands 2005, Canada 2007 and Turkey 2013.

Argentina–Chile relations: Argentina–Chile relations refers to interstate relations between the Republic of Chile and the Argentine Republic.  Argentina and Chile share the world's third-longest international border, which is 5300 km long and runs from north to the south along the Andes mountains.  Although gaining their independence during the South American wars of liberation, during much of the 19th and the 20th century relations between the countries were chilled as a result of disputes over the border in Patagonia.  In recent years relations have improved dramatically.  Despite increased trade between the two countries, Argentina and Chile have followed quite different economic policies.  Chile has signed free trade agreements with countries such as China, the USA, Canada, South Korea and the EU and is an active member of the APEC, while Argentina belongs to the Mercosur regional free trade area.  Both countries are members of the Union of South American Nations.

Geography of Chile: The geography of Chile is extremely diverse as the country extends from a latitude of 17° South to Cape Horn at 56° (if Chilean claims on Antarctica are included Chile would extend to the South Pole) and from the ocean on the west to Andes on the east.  Chile is situated in southern South America, bordering the South Pacific Ocean and a small part of the South Atlantic Ocean.  Chile's territorial shape is among the world's most unusual.  From north to south, Chile extends 4270 km , and yet it only averages 177 km east to west.  On a map, it looks like a long ribbon reaching from the middle of South America's west coast straight down to the southern tip of the continent, where it curves slightly eastward.  Diego Ramírez Islands and Cape Horn, the southernmost points in the Americas, where the Pacific and Atlantic oceans turbulently meet, are Chilean territory.  Chile's northern neighbors are Peru and Bolivia, and its border with Argentina to the east, at 5150 km , is the world's third longest.

Operation Soberanía: Operación Soberanía (Operation Sovereignty) was a planned Argentine military invasion of Chile started on 22 December 1978 due to the Beagle conflict dispute.  The invasion was halted after a few hours and Argentine forces retreated from the conflict zone without a fight.  Whether the Argentine infantry actually crossed the border into Chile has not been established.  Argentine sources insist that they crossed the border.

José Miguel Carrera: José Miguel Carrera Verdugo (October 15, 1785 – September 4, 1821) was a Chilean general, member of the prominent Carrera family, and considered one of the founders of independent Chile.  Carrera was the most important leader of the Chilean War of Independence during the period of the Patria Vieja ("Old Republic").  After the Spanish Reconquista ("Reconquest"), he continued campaigning from exile.  His opposition to the leaders of independent Argentina and Chile San Martin and O'Higgins respectively made him to live in exile in Montevideo.  From Montevideo Carrera traveled to Argentina where he joined the struggle against the unitarians.  Carreras small army was eventually left isolated in the Province of Buenos Aires from the other federalist forces.  In this difficult situation Carrera decided to cross to native-controlled lands all the way to Chile to once for all overthrow Chilean Supreme Director O'Higgins.  His passage to Chile, which was his ultimate goal, was opposed by Argentine politicians and he engaged together with indigenous tribes, among the Ranquels, in a campaign against the southern provinces of Argentina.  After the downfall of Carreras ally, the Republic of Entre Ríos, and several victories against the United Provinces of the Río de la Plata Carrera's men were finally defeated by numerically superior forces near Mendoza.  Carrera was then betrayed by one of his Argentine helpers, leading to his capture and execution in that city.  José Miguel Carrera was of Basque descent.

1856 Argentina–Chile treaty: The Treaty of Peace, Friendship, Commerce and Navigation of 1856 between Chile and Argentina (Spanish: "Tratado de paz, amistad, comercio y navegación entre la República de Chile y la Confederación Argentina" ) was the first boundary treaty between Argentina and Chile.  It established that the boundaries should be based on the uti possidetis principle based on what each country possessed before independence in 1810.  It also postponed the solution of disputes into the future.  Article 39 of the treaty proposed the use of direct diplomatic negotiations and arbitration to resolve disputes.  This treaty was later declared null and void in the Boundary treaty of 1881 between Chile and Argentina, but the mechanism for solving disputes where inherited by the 1881 treaty.

Supporting paragraphs: Operation Soberanía Beagle conflict
Answer: Picton, Lennox and Nueva islands