Three times in the past 30 years Colombian governments have tried and failed to negotiate peace with the Revolutionary Armed Forces of Government (FARC), a onetime Marxist guerrilla group that embraced kidnapping, drug trafficking and terrorism. The most dismal episode began in 1999, when the government declared a cease-fire and ceded the FARC a safe zone the size of Switzerland, only to watch as the group used the space to regroup, recruit and cultivate coca while refusing to bargain seriously.

That history made many Colombians appropriately wary when the current government, under President Juan Manuel Santos, announced plans for new negotiations it hopes will lead to the FARC’s demobilization. This time, however, there is more reason for optimism — thanks in significant part to the success of U.S.-Colombian collaboration over the past decade.

Since the last peace talks failed, the United States has supplied some $8 billion to Colombia, helping it to double the size of its army, train elite units, acquire helicopters and other advanced equipment, and take the fight to the FARC. The movement has suffered crippling blows, including the death of its founder.

Santos is betting that what remains of the FARC will follow the example of other Latin American armed movements that have transformed themselves into democratic political parties. He is right to try.

There are, nevertheless, some big obstacles. FARC leaders have said that when talks begin in Oslo on Oct. 8, they will seek a cease-fire; that could allow them to repeat their previous dilatory strategy.

Santos has said that military operations will go on and that the talks will be limited to a few months. Perhaps the FARC will give up violence and criminality. If not, the United States should support Colombia’s military in a renewed war against this menace.