Place chicken breast in a large saucepan; cover with cold water. Bring to a boil, reduce heat, and simmer 10 minutes or until chicken is done. Remove chicken from pan; let cool 30 minutes. Shred chicken breast.
Heat 2 teaspoons oil in a large skillet over medium-high heat; add 1/2 cup onion. Sauté 6 minutes or until golden brown. Remove onion from pan; combine shredded chicken and onion.
Heat remaining 1 teaspoon oil in skillet; add remaining 1 cup onion and garlic. Cover and cook 5 minutes or until onion is tender. Stir in chipotle and remaining ingredients. Cover and simmer 20 minutes.
Process chipotle mixture in a blender until smooth. Combine chicken and chipotle sauce. Serve with fresh sopes.