The Doha-based state airline announced the stock purchase late Wednesday.
LATAM was created when Chile's LAN took over Brazil's TAM in 2012. The airline flies to some 140 destinations in 25 countries.
LATAM stock closed at $8.42 a share Wednesday, up 1.6 percent.
Qatar Airways operates a fleet of 192 aircraft out of its hub in the vast new Hamad International Airport in Doha, which is preparing to host soccer's World Cup in 2022.
It is one of the Middle East's biggest carriers, along with Dubai-based Emirates Airline and the Abu-Dhabi based Etihad Airways. The three airlines increasingly have challenged Western airlines in long-haul flights.