Combine juices, cilantro, tarragon, ancho chile, cayenne, and 1/2 teaspoon salt and pepper in a bowl. Add chicken, cover, and refrigerate for 1 to 2 hours.
Heat grill or broiler to medium high. Sprinkle chicken with 1/2 teaspoon salt and 3/4 teaspoon pepper. Cook 3 or 4 minutes per side, or until cooked through. Cover; set aside in a warm place.
Using tongs, toast tortillas over a flame, quickly flipping them from side to side until lightly golden. Cut each chicken breast half into 5 slices. On bottom third of each tortilla, place 5 chicken slices, several strips of lettuce, and 3 tablespoons mango salsa. Roll up, and serve with remaining salsa and sour cream.