Heat a large pot over medium heat. Add the oil. Season the chicken with salt and pepper. Add the chicken to the pot and cook until browned, turning as needed, about 3 minutes per side (you may need to cook in batches). Remove the chicken to a baking sheet or plate as done.
Add the onions and a pinch of salt to the pot and saute about 2 minutes. Add the garlic, carrot and celery and saute about 2 minutes.
Add the liquid to the pot and stir with a wooden or other heatproof spoon, scraping up the bottom of the pot for the tasty bits. Add the tomatoes and beans and bring to simmer.
Return the chicken to the pot and bring to a simmer. Cook until the chicken is cooked through, 10 to 15 minutes. Or, bake at 350 degrees F, uncovered, until the chicken is cooked through.
Remove the pot from the heat and stir in the greens if you have them.
For more ingredient substitution ideas, see the article below.