Trim excess fat from chicken thighs and season them generously with salt and pepper. Heat oil in a large, lidded skillet over medium-high flame. Add chicken skin side down and sauté until golden brown, about 5 minutes. Turn chicken, reduce heat to medium and cook for about 3 minutes. Transfer to a plate (they won’t be cooked through—that’s okay, they’re going back in the pan later).
Add onion to pan and cook, stirring frequently, until it just starts to soften, about 3 minutes. Don’t let it brown—reduce heat if needed. Add rice to pan and cook, stirring frequently, for another 3 minutes. Clear a space in the middle of the pan and add garlic. Cook, stirring constantly, for about 45 seconds.
Add broth and tomatoes to pan and stir to combine. Nestle chicken thighs into the rice. Bring to a boil, reduce to a simmer and cook, covered, for about 20 minutes.
Remove chicken to a plate and add beans, cilantro and lime juice to pan, stirring to combine. If the rice has absorbed too much liquid, stir in a little water. Taste and adjust seasonings with salt and pepper.
Return chicken to pan and cover. Cook until everything is warmed through, about 5 minutes.
To serve, spoon rice and beans mixture onto plates and top with a chicken thigh.