The Spanish Conquistador who advanced south from Peru into what is now Chile to conquer it, Pedro de Valdivia, fought against the native Mapuche in a vain attempt to subdue them (he managed to push south of the Bio-Bio River but this territory would remain in the hands of the natives until the 1870s).
During his campaing into northern Chilean Patagonia, Valdivia founded a city in 1552 which he named “El Imperial” (The Imperial) in honor of his king and emperor, Charles the Vth of Germany (and Ist of Spain).
He gave it that name because, there he had “discovered certain rudely-carved figures, with somer resemblance to the double-heade eagle of Austria” (Charles was a Hapsburg, of Austrian blood). 
The interesting fact is that these “eagles” had been carved by the local Mapuche natives and therefore had no connection whatsoever with Europe or the House of Austria. It is likely that they were not even eagles, but “condors”.
The two-headed condor motif is quite common among the Andean cultures such as the Inca in Peru and the Diaguita or Kakan people of northwestern Argentina. Perhaps the bicephalic condor symbol was introduced into the area during the period of Inca domination (ca. 1430-1530).
Copyright © 2010 by Austin Whittall
Or it may have been a pre-Inca symbol, part of the Mapuche mythology.
Another option is that the Spaniards assigned an “eagle” morphology to a non avian sculpture, believing that they were two-headed eagles, when they may have been something else.
The two headed eagle is also found among the Alaska natives, but it is very likely that it was acquired from the Russians, whose imperial coat of arms bore a two headed eagle. 
However, the two headed condor motif exists among the Mapuche people.
In Neuquén, Argentina, there is a legend about Domuyo Volcano involving a native princess, Pirepillan, who was held captive on its summit by a jaguar and a “two headed condor”. 
 Smith, E., (1855), The Araucanians.New York: Harper. Bros. pp. 142.
 Northwest Coast Archaeology. Two Views of Double-Headed Eagles. 01.03.2010.
 Melantoni, E., Las termas de Copahue pp. 3.
 Camprubí Bueno, L., (2010). Viaje alrededor del Imperio: rutas oceánicas, la esfera y los orígenes atlánticos de la revolución científica. El Catoblepas, 95. 01.2010. pp.1.
Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia2010 International Year of Biodiversity Copyright 2009-2010 by Austin Whittall ©