Slice chicken breasts into ½-inch thick pieces and season with the black pepper. Heat oil over medium-high heat in a large skillet.
Add chicken and cook for about 3 minutes on each side until lightly browned, turning each piece once.
In a medium mixing bowl, combine the salsa, peanut butter, lime juice, soy sauce, ginger, garlic, and cayenne pepper, if using, with a whisk. Add the salsa mixture to the skillet.
Cover, and cook for another 10 minutes on medium heat or until chicken is fully cooked.
Use a slotted spoon to remove the chicken from the skillet, and place on a serving platter. Spoon the sauce from pan over the chicken. Garnish with peanuts, cilantro, and lime wedges, if desired.