You need to look at the per capita GDP and per capita GDP adjusted for purchasing power parity (PPP) to measure the relative economic strength of countries regardless of population disparities. Chile should have a smaller GDP; it has 16 million people compared with Brazil's 180. However, its GDP is proportionally higher:
According to the IMF Brazil is 6th world-wide, while Chile is 39, even lower than the other key player of the region: Argentina (27).