Yet no other American military project in sub-Saharan Africa has generated the attention — and the high expectations — as the pursuit of Mr. Kony, partly thanks to a wildly popular video on Mr. Kony’s notorious elusiveness and brutality, “Kony 2012,” that set YouTube records with tens of millions of hits in a matter of days. Gen. Carter F. Ham, the overall commander of American forces in Africa, has a “Kony 2012” poster tacked to his office door. As one American official put it: “Let’s be honest, there was some constituent pressure here. Did ‘Kony 2012’ have something to do with this? Absolutely.”

Mr. Kony started out in a northern Uganda village more than 25 years ago as a Catholic altar boy who spoke in tongues. People said he was a prophet. He went on to form a rebel force, the Lord’s Resistance Army, bent on overthrowing Uganda’s government and ruling the country with the Ten Commandments. Soon enough, though, Mr. Kony was breaking every one.

His fighters mowed down impoverished villagers, sawed off lips, and kidnapped thousands of children, brainwashing them for use as tiny killing machines. Mr. Kony often donned wigs and costumes, saying he was possessed by spirits including one named, “Who Are You?” In 2006, Ugandan troops pushed Mr. Kony out of Uganda into the lawless borderlands where the Democratic Republic of Congo, the Central African Republic and what is now South Sudan meet.

By this point, Uganda had become one of America’s closest African allies, and when the United States was deeply worried about Somalia’s becoming a terrorist sanctuary, Uganda was the first country to step forward with peacekeepers, scoring major Pentagon points.

In December 2008, the new American military command for Africa, known by the acronym Africom, helped plan an attack on Mr. Kony’s camp in Congo, dispatching a team of military advisers to Uganda. But Mr. Kony escaped before the Ugandan helicopter gunships even took off — apparently he had been tipped off. Worse, his army slaughtered hundreds of nearby villagers in revenge, leaving behind scorched huts and crushed skulls.

The American government continued running a semicovert logistics and intelligence operation to extend the Ugandan army’s reach so it could chase Mr. Kony across the region. The United States has also pumped in more than $500 million in development aid to northern Uganda, turning a former battlefield into a vibrant piece of the Ugandan economy with new banks and hotels.