Place chicken breasts in a large saucepan. Pour in just enough water to cover.
Place chicken over medium-high heat and bring to a boil. Keep at a rapid simmer until the chicken meat is no longer pink, about 10-12 minutes. You can always prepare chicken breast however you please, just make sure they are cooked before shredding.
Transfer chicken breasts to a bowl (draining any excess water first). Once the chicken breasts are cool, use two forks to shred them thoroughly.
Heat grapeseed oil in a small saucepan over medium heat. Add onion and cook, stirring occasionally, until the onion is translucent (2-3 minutes).
Add carrots; cook for another minute.
Add the shredded chicken and BBQ sauce to the onion and carrots. Bring to a gentle boil until the BBQ sauce reduces, usually about 5-10 minutes.
Scoop chicken into lettuce leaves. Drizzle with additional BBQ sauce if desired.