Late on Sept. 6, 2005, a private plane carrying the Canadian mining financier Frank Giustra touched down in Almaty, a ruggedly picturesque city in southeast Kazakhstan. Several hundred miles to the west a fortune awaited: highly coveted deposits of uranium that could fuel nuclear reactors around the world. And Mr. Giustra was in hot pursuit of an exclusive deal to tap them. Unlike more established competitors, Mr. Giustra was a newcomer to uranium mining in Kazakhstan, a former Soviet republic. But what his fledgling company lacked in experience, it made up for in connections. Accompanying Mr. Giustra on his...