Actually, we don't have to speculate on US reaction--at least we know how FDR reacted to rumors of a sale some years later:
"Early in 1939 Under Secretary of State Sumner Welles informed the President of reports from Ambassador Armour that the government of Chile was thinking about selling Easter Island, apparently not having considered 'that the sale of this island to a non-American power would violate any hemispherical doctrine of non-transfer of territory or prejudice the defense of the continent.' Welles suggested offering to purchase or lease the island, and inquired about price. Roosevelt pointed out the possible importance of Easter Island as an air base, and agreed that 'it should, therefore, under no circumstances be transferred to any non-American nation,' but he opposed the thought of further territorial expansion in the Hemisphere by the United States. Instead he advocated some form of 'joint trusteeship of the American Republics" over not only Easter but also the Galapagos and perhaps Cocos Island to preserve them for colonization and for natural science and to keep them out of the hands of non-American powers. The cost of administration should be borne by the trustees in proportion to their national wealth...'" John A. Logan, *No Transfer: An American Security Principle,* (New Haven: Yale University Press 1961), p. 131.
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Here is the text of FDR's letter to Welles:
President Roosevelt to the Under Secretary of State (Welles)
Washington, March 25, 1939.
Memorandum
In regard to Easter Island:
1.
It is a definite possibility as a stopping place for trans-South Pacific planes, commercial or military.
2.
It should, therefore, under no circumstances, be transferred to any non-American nation.
3.
I doubt at this time the political wisdom of its purchase by the United States, and also the possibility of getting any large appropriation through the Congress.
4.
Have you considered a different angle? Easter Island is unique in possessing remains of prehistoric men—the great recumbent stone figures which have never yet been adequately explained. No serious scientific excavation work has been done on the Island. It is, therefore, of the greatest importance that it be preserved to science for all time. In this respect it is a little like the Galápagos Islands.
62
5.
Would it be possible to tie up Easter Island and the Galápagos in a Pan-American trusteeship; the Islands to be preserved for all time against colonization and for natural science? Ecuador and Chile (if a reasonable sum could be arrived at) would be paid for the Islands over a period of years, the sovereignty to vest in the trustees; the trustees to protect them and prevent their use for military purposes. I do not like the idea of a lease. The payments would be made by all the American Republics over a period of years and in proportion to the total wealth of the Republics. This would put, of course, the greatest burden on the United States.
6.
Cocos Island
63 could be included, for it has no military value to us but might have military value to a non-American power as a temporary base in war operations.
As I remember Easter Island, it has no harbor. Will you let me have some information regarding it? It may not even be available for sea planes or land planes.
F[ranklin] D. R[oosevelt]
https://history.state.gov/historicaldocuments/frus1939v05/d486
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I think it is clear from this that the US would oppose the sale of Easter Island to *any* non-American power, including the UK. Indeed, as I noted some years ago in soc.history.what-if, the US quire definitely opposed any new British acquisitions in the Western Hemisphere in the twentieth century:
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"In 1920 the Danish government asked the UK to recognize its right to extend its political and economic interest in the whole of Greenland--a claim to sovereignty already acknowledged by the US as a condition of the cession of the Danish West Indies four years earlier. The British government replied that it would agree to this proposition only if granted the right of pre-emptive purchase in case Denmark should consider disposing of Greenland. When word of the British demand reached Washington, Secretary of State Colby strongly objected, and in deference to the US objection, the UK softened its conditions.
"Even in 1940, when one might think after Hitler's occupation of Denmark, the US might welcome a British or Canadian occupation of Greenland, instead the US was anxious to prevent precisely this event, while not yet ready to dispatch troops itself. (Eventually it did, of course, but only after keeping the question in suspense for a year.) This was partly out of a desire to deny Japan an excuse for a 'protective' occupation of the Dutch East Indies should Hitler make his expected assault on Holland. But it was also a product of the US belief that Greenland was part of the Western Hemisphere, and that the Monroe Doctrine (including the no-transfer policy) applied. Hull specifically reminded Lord Lothian of Colby's 1920 note, which Hull called an 'express application of the Monroe Doctrine by the United States.'"
http://groups.google.com/group/soc.history.what-if/msg/7e06b89fb2c0843d
