I am posting this on behalf of Miguel, who is quite knowledgeable of the history of the Arabian horse breed in Chile, where he tells me that he believes the Chilean registry is the oldest of all those in South America. The Chilean registry includes Peru, and is said to have begun in in 1872, the details of which you will find below.
An unpublished picture of the imported mare *Hadriya
Courtesy of Nina Heidke, who continues to breed the horses of her partner Lee Oellerich, including descendants of *Hadriyah (*Jalam Al Ubayyan x *Savannah) of the Dahmah Shahwan strain.