Heat a large wok or nonstick skillet over medium-high heat. Add 2 teaspoons oil; swirl to coat. Add shallots and sauté 2 minutes. Add bell pepper and sauté 1 minute. Add garlic and sauté 30 seconds. Remove shallot mixture from pan and set aside.
Add remaining 2 teaspoons oil to wok or pan; swirl to coat. Add chicken and cook 5 minutes or until browned, stirring to crumble. Drain well. Return chicken to wok or pan over medium heat. Add chiles and cook 1 minute. Add shallot mixture to pan. Stir in fish sauce and next 3 ingredients (through black pepper); cook 1 minute or until thoroughly heated. Remove pan from heat; stir in basil and juice.
If using the lettuce leaves, place about 1/3 cup of the mixture in each lettuce wrap. Serve with lime wedges.