In a 3- to 4-quart pan over medium-low heat, stir pecans often until lightly browned, 3 to 4 minutes. Pour into a small bowl.
In the same pan, cook rice in water as directed on package, until tender to bite, about 25 minutes. Reserve seasoning packets for another use.
Meanwhile, slice mango lengthwise down each side of pit to remove fleshy cheeks. On the flesh side of each cheek, cut down to the peel (but not through it) in a crosshatch pattern to make 3/4-inch cubes. With a large metal spoon, scoop cubes from peel. Also trim fruit off pit and dice it.
Mix mango nectar and vinegar. Add to warm or cool rice and mix lightly. Add pecans, mango, chicken, and chopped mint; gently mix. Add salt and pepper to taste.
Spoon into bowl and garnish with mint sprigs.