While the chicken is boiling, in a separate pan, heat the oil over medium heat, add rice and cook, stirring occasionally, until browned, about 2 to 3 minutes, being careful not to let it burn. Add onion and continue cooking until onion is translucent, about 2 minutes. Add tomato and cook for an additional 3 minutes. Add mixture to chicken pot.
Add carrots, celery, and potatoes to soup and let come to a boil; reduce heat. Let simmer until vegetables cook through, about 20 to 30 minutes. Add tomato sauce, cilantro, and safflower petals during the last 5 minutes.
Ladle soup, including a piece of chicken for each serving, into bowls and serve with lime wedges, warm corn tortillas, and salsa casera.
Feel free to add additional veggies like chayote, Mexican zucchini, and cabbage. This rustic soup is so delicious and customizable.
Refrigerate, covered, for up to one week. It is also an excellent candidate for freezing and will keep in the freezer for up to three months.