The Chilean navy is investigating allegations of xenophobia, after a video emerged apparently showing marines chanting offensive slogans.
About 40 men appear jogging along a beach while chanting that they would "kill Argentines, shoot Bolivians and slit the throats of Peruvians".
The ministry of defence promised to punish those responsible and ordered an investigation within 24 hours.
Historically, Chile's relations with its three neighbours have been poor.
It fought Bolivia and Peru in the 19th Century and still has border disputes with both of them.
Tensions over three small islands brought Chile and Argentina to the verge of armed conflict in the 1970s.
The head of the Chilean navy, Admiral Edmundo Gonzalez, described the video as unacceptable.
Writing on Twitter, he promised "maximum sanctions" for those responsible for the chanting, if they are confirmed to be in the armed forces ranks.
Replying to another user who said that those who attended military academies know that "such chants are sung everyday while jogging", Admiral Gonzalez said that the instruction was to sing "military chants".
'We'll drink their blood'
"Not improvisations. That's the sin of that video," he added.
But the user replied that the chant on the video was not an improvisation, and quoted an alleged missing line: "and we'll drink their blood".
Chile's acting Defence Minister, Alfonso Vargas, said that his country had been "a victim of similar situations in other countries and we didn't like it".
Mr Vargas added that the chant is not in line with Chile's policies towards their "brotherly" neighbours.
The video has made headlines in many South American countries, especially in the neighbours involved.
Chile still has an unsettled border issue with Argentina, involving the limits of the southern Patagonian ice field.
Bolivia also peacefully disputes access to the Pacific Ocean since losing its coast after a war with Chile in the 19th Century.
The dispute with Peru is over a maritime border in the Pacific, which the Peruvians took to the International Court of Justice in The Hague.
Correction 8 February: Clarifiying 1970s tension with Argentina