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.
Loved this!! Very flavorful. I added chopped toasted peanuts, swapped shredded cabbage for the lettuce. I also skipped the cucumber after reading some reviews, and instead sliced it and tossed it with seasoned rice wine vinegar, which made a nice side. Using really thin tortillas is key, or rice paper if you can find it.