Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery. Cook for 5 minutes until the vegetables begin to soften.
Stir in the garlic, rosemary, and thyme. Cook for 1 minute until fragrant.
Add the chicken thighs, bay leaf, and water. Bring to a boil, then reduce to a simmer. Cover and cook for 25 minutes until the chicken is fully cooked.
Remove the chicken from the pot. Shred the meat and discard the bones and skin. Return the shredded chicken to the pot.
Stir in the cannellini beans and kale. Simmer uncovered for 8 minutes until the kale wilts. Season with salt and pepper.