Heat oil in a large, nonstick skillet over medium-high heat. Add chicken; cook for 5 minutes on each side or until done. Remove from pan; cool. Shred chicken into bite-size pieces. Place chicken, cucumber and bell pepper in a large bowl.
Process sugar, ginger, lime juice, soy sauce, salt, red pepper and garlic in a blender until smooth. Add peanut butter and water; blend. Combine peanut butter and chicken mixtures; stir. Add cilantro; toss.
Warm tortillas according to package directions. Spoon 1/2 cup chicken mixture and 1/2 cup lettuce onto each tortilla; roll up.