Combine 1/4 cup of the yogurt, chile powder, curry powder, 1/4 teaspoon of the lime juice, garlic and salt in a wide, shallow baking dish. Add chicken, turn to coat, cover and refrigerate for at least 1 hour.
Meanwhile, put remaining yogurt, two-thirds of the mango and remaining 1/2 teaspoon lime juice into a blender; puree until smooth to make a sauce, then set aside.
Preheat oven to 375°F.
Bake chicken until just cooked through, about 25 minutes.
Transfer to plates, top with some of the yogurt sauce and garnish with remaining mango. Serve extra sauce on the side.