Combine chicken breasts, 1/2 an onion, celery, and parsley with cold water and chicken bouillon in a saucepan. Bring to a boil. Reduce heat and simmer the stock until chicken is no longer pink in the center, 20 to 25 minutes.
Remove chicken from the stock and shred with a fork. Strain stock and discard onion, celery, and parsley. Return stock to the saucepan.
Heat oil in a skillet over medium heat. Add chopped onion and garlic; cook and stir until transparent, about 3 minutes. Add tomatoes and cook until tender, about 5 minutes. Let cool slightly, about 5 minutes. Pour mixture into a blender; add 1 cup stock. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend.
Pour tomato mixture into the saucepan of stock; add chickpeas and carrots. Let simmer until carrots are nearly softened, about 10 minutes. Stir in the shredded chicken and chipotle peppers. Let simmer until flavors blend and carrots are tender, about 10 minutes more. Season with salt and serve with avocados, lime quarters, and Oaxaca cheese on the side.