This gigantic piece of real estate just happens to be atop the Guarani Aquifer, one of the world's largest aquifer systems and an important source of fresh water for its people.
From the Wikipedia entry:
The Argentine film called Sed, Invasión Gota a Gota ("Thirst, Invasion Drop by Drop"), directed by Mausi Martínez, portrays the military of the United States as slowly but steadily increasing its presence in the Triple Frontera (Triple Frontier, the area around the common borders of Paraguay, Argentina and Brazil). The overt reason for the increasing presence of U.S. troops and joint exercises, mainly with Paraguay, is to monitor the large Arab population which resides in the area. However, Martínez alleges that it is the water which brings the Americans to the area, and she fears a subtle takeover before the local governments even realize what is going on.
Similar concerns were lifted following both the signature of a military training agreement with Paraguay, which accorded immunity to U.S. soldiers and was indefinitely renewable (something which had never been done before, while Donald Rumsfeld himself visited Paraguay and, for the first time ever, Paraguayan president Nicanor Duarte Frutos went to the White House), and the construction of a U.S. military base near the airport of Mariscal Estigarribia, within 200 km of Argentina and Bolivia and 300 km of Brazil. The airport can receive large planes (B-52, C-130 Hercules, etc.) which the Paraguayan Air Force does not possess.  . The governments of Paraguay and the United States subsequently ostensibly declared that the use of an airport (Dr Luís María Argaña International) was one point of transfer for few soldiers in Paraguay at the same time. According to the Argentine newspaper Clarín, the U.S. military base is strategic because of its location near the Triple Frontier, its proximity to the Guaraní Aquifer, and its closeness to Bolivia (less than 200 km) at the same "moment that Washington's magnifying glass goes on the Altiplano [Bolivia] and points toward Venezuelan [president] Hugo Chávez — the regional devil according to the Bush administration — as the instigator of the instability in the region" (El Clarín ).