For mole, halve chile peppers; remove stems and seeds. Coarsely chop peppers; set aside. In a large skillet cook onion and garlic in hot oil over medium-high heat until onion is tender. Add the dried peppers and the water. Reduce heat to medium. Stir in chocolate. Cook and stir, uncovered, for 3 to 5 minutes or until thickened and bubbly; cool slightly. Transfer mixture to a food processor or blender; cover and process or blend until mixture forms a smooth paste. Set aside to cool. Reserve 1 to 2 tablespoons of the mole.
Sprinkle chicken with salt. Using a sharp knife, carefully cut a horizontal slit two-thirds of the way through each breast half. Spread inside surfaces of the chicken with cooled mole; fold closed. Rub outside surfaces with reserved 1 to 2 tablespoons mole.
For a charcoal grill, grill chicken on greased rack of an uncovered grill directly over medium coals for 12 to 15 minutes or until chicken is tender and no longer pink (170 degrees F), turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place chicken on greased grill rack over heat. Cover and grill as above.) Slice chicken.
Meanwhile, in a small bowl stir together avocado, mayonnaise, cayenne pepper, and the 1/8 teaspoon salt.
To assemble sandwiches, spread avocado mixture on cut sides of rolls. Fill with chicken and, if desired, lettuce, tomato, and papaya.