To butterfly the chicken breast, place them flat on a cutting board with your hand on top. Using a sharp knife, slice most of the way into the thicker side of the breast and slice along until you reach the thinner side. Be careful not to cut through the entire breast; just cut enough to be able to open the breast like a book.
Combine 1/4 cup yogurt,1/4 cup of cilantro, half of the lime juice, cayenne pepper, and garlic. Coat chicken breast with this mixture, marinate for at least 1 hour.
While chicken marinates, purée remaining yogurt, 2/3 of cubed mango, 1/2 teaspoon lime juice, and 1 cup cilantro in blender.
Bake chicken in a glass baking dish for 25-30 minutes.
Place chicken on serving plates, pour on sauce, and sprinkle with mango and extra sauce on side.
Garnish with more cilantro and lime and season to taste.