Heat olive oil in a large pot over medium heat. Add the onion, carrots, celery, and garlic. Cook until the vegetables are softened, about 5 minutes.
Add the chicken pieces to the pot and cook until browned on all sides, about 5 minutes.
Pour in the chicken broth and bring to a boil. Reduce heat to low and simmer for 20 minutes.
Add the white beans and dried thyme to the pot. Season with salt and pepper to taste. Cook for an additional 10 minutes.
To serve, ladle the soup into bowls and top each serving with a spoonful of pesto.
Enjoy!