On a large plate, combine the peanuts, bread crumbs, cilantro, and ½ teaspoon each salt and pepper. Thread each strip of chicken onto a skewer and coat with the peanut mixture, pressing gently to help it adhere.
In batches, heat the oil in a large nonstick skillet over medium heat and cook the skewers until golden, 2 to 3 minutes on each side. Transfer to a plate as they are cooked and add more oil to the skillet as necessary.
In a small bowl, combine the mayonnaise and chili-garlic sauce. Serve with the chicken.