Rinse chicken. In a 3- to 4-quart pan over medium-high heat, bring chicken broth, 2 tablespoons lime juice, and chipotle purée to a simmer. Add chicken breasts, adjust heat to maintain simmer, and cook until chicken is no longer pink in the center of the thickest part (cut to test), 10 to 15 minutes. With tongs, transfer chicken to a bowl; reserve broth. When chicken is cool enough to handle, tear or cut into bite-size shreds.
Meanwhile, heat oil in an 8- to 10-inch frying pan over medium heat. When hot, add 1/4 cup onion and the garlic and stir frequently until onions are limp, about 5 minutes. Add reserved chicken broth and tomato sauce and bring to a boil; reduce heat and simmer to blend flavors, about 5 minutes. Pour sauce over chicken and mix to coat.
In a small bowl, mix remaining 1 cup minced onion, remaining 1 tablespoon lime juice, cilantro, and salt to taste.
In a 3- to 4-quart pan over medium-high heat, warm pinto beans until hot. Stack tortillas and wrap in microwave-safe plastic wrap. Heat in a microwave oven at 50 percent power until steaming, about 1 1/2 minutes. Remove plastic and wrap tortillas in a towel to keep warm. Serve tortillas, beans, chicken mixture, and onion relish separately, letting each person fill tacos as desired.
To make chipotle purée, whirl a 7-ounce can of chipotle chilies, including the adobo sauce, in a blender or food processor until smooth. Scrape into a plastic container and store airtight in the refrigerator up to 1 week or in the freezer for several months.