Lan Chile is part of LAN Group which covers Lan Chile, Lan Peru, Lan Ecuador, Lan Argentina and Lan Dominicana. All pilots are hired and trained by Lan Chile but the vast majority are residents or nationals of thier repective countries. Lan is a FAR 129 airline ,(foreign air carrier), which requires an ICAO ticket from the respective country. Not very hard to get. Just a whole bunch of burocratic paperwork and a serious medical exam that lasts about 2 days.
Like Free bird says; LAN owns Florida West Airlines in Miami FL. They are a FAR 121 carrier and hire pilots with FAA licenses.
Lan is by far the best airline in South America.
Hope it helps.