Soak 24 bamboo skewers about 6 inches long in a bowl of cold water at least 20 minutes. Cut chicken breasts into 24 thin strips. In a food processor, mince onions and garlic. Remove half of this mixture to a small bowl and reserve. Add soy sauce and 3 Tblsp. lime juice to food processor. Combine well and coat chicken strips. Cover and refrigerate 2 hours. Return reserved onion and garlic mixture to food processor. Add remaining 1 Tblsp. lime juice, black pepper, peanut butter, coconut milk, brown sugar, dried hot red peppers, and anchovy paste. Process until smooth. Transfer mixture to a nonstick saucepan and cook over low heat 10 minutes. Some oil will separate out of the sauce. Gently blot off excess with a paper towel. Remove sauce to a small bowl for serving. Prepare a medium-hot fire in a barbeque grill or preheat broiler. Thread chicken strips onto wet bamboo skewers. Grill or broil until chicken is cooked through, about 5 to 7 minutes. Serve satay on their skewers with sauce on the side for dipping.