SEPTEMBER 11th is best known for al-Qaeda’s attack on the World Trade Centre and the Pentagon in 2001. But in Latin America the date is remembered for another act of villainy. On that day in 1973 General Augusto Pinochet staged a military coup against the chaotic Socialist government of Salvador Allende in Chile.

This ushered in a 17-year dictatorship that murdered 3,000 people and tortured many more. The coup was hatched in Chile. But it was backed by Richard Nixon, who had earlier ordered the CIA to “make the economy scream”. It was one of the more notorious of many interventions by the United States in Latin America, starting with a war against Mexico in 1846, including other coups during the Cold War and culminating in the invasion of Panama in 1989 to topple Manuel Noriega, a former American intelligence asset turned ally of drug traffickers.

Intervention was far from continuous. Presidents such as Franklin Roosevelt and John Kennedy sought partnerships south of the Rio Grande (as did Barack Obama and George W. Bush), and support for democratic government has underpinned the United States’ policy towards Latin America since the end of the cold war. But in the region this legacy forged enduring and widespread resentment. It has made non-intervention in the affairs of other states Latin governments’ default diplomatic position, attenuated only timidly by the adoption of the defence of human rights and democracy in the Inter-American Democratic Charter of 2001.

This history explains why the region expressed alarm when Donald Trump mused a year ago about military action to overthrow the dictatorial government of Nicolás Maduro in Venezuela. The main Latin American governments refused to recognise a fraudulent election in May in which Mr Maduro re-elected himself. But they argue that yanqui threats merely strengthen him. They trust in diplomatic pressure and opposition within the country to restore democracy.

The problem is that Venezuela is no longer just a danger to itself. It is a pressing regional issue. Since 2016 over 2.3m Venezuelans have fled, mainly to neighbouring countries, “due largely to lack of food... medicines and health care, insecurity and political persecution”, as Michelle Bachelet, a former Chilean president and now the UN High Commissioner for Human Rights, put it this week. On the whole, South American countries have received the migrants with great generosity. But their arrival inevitably puts pressure on public services that are already strained, and arouses fears of competition for jobs. Meanwhile, Venezuela has become a base for organised crime and drug smuggling.

How can this nightmare end? In the past Venezuela’s combination of hyperinflation, economic collapse and an unpopular and now illegitimate government would have prompted a pronunciamiento (bloodless coup), with or without American help. According to the New York Times, a United States government official met three times in the past year with a group of army officers who planned such a power-grab. But in the end the Trump administration denied them support.

Although a one-off meeting to seek information is not unusual, the purpose of the subsequent dealings is not clear, says Frank Mora, who served under Mr Obama. Marco Rubio, a Republican senator, said recently that there was a case for military action to topple Mr Maduro. Such hawks should be careful what they wish for, warns Mr Mora. Venezuela’s top brass have much to lose, not least their cocaine business. There is no guarantee that a coup would lead to a swift and bloodless restoration of democracy.

Were this indeed to happen, many in Latin America would doubtless breathe a quiet sigh of relief. But no government wants its fingerprints on a putsch. Many prominent Latin Americans still insist that the Venezuelan regime will collapse of its own accord. “A foreign intervention is never justified [unless] there was a massacre or genocide,” says Ottón Solís, an adviser to Costa Rica’s government. This is a widely shared view.

But the regime’s demise is far from inevitable. Mr Maduro is driving opponents out. Tellingly, the coup-plotters asked their American contact for encrypted radios. Protected by Cuban counter-intelligence agents, Venezuela’s government pounces on dissent. Scores of would-be military mutineers have been arrested.

Latin America has good reason to reject American military intervention in Venezuela. But it faces a stark choice. Either it mobilises global support to force serious talks in which Mr Maduro agrees to go, or it will have to live with the consequences of his country’s implosion.