Brown the chicken: Heat olive oil in a large pot over medium heat. Add chicken and season with salt and pepper. Cook until golden brown on all sides (about 5-7 minutes). Remove from pot and set aside.
Combine ingredients: Return chicken to pot. Add carrots, celery, potatoes, thyme, bay leaf, chicken broth, and tomato paste. Bring to a boil, then reduce heat to low.
Simmer: Cover and simmer for 30 minutes, or until chicken and vegetables are tender.
Season and serve: Season with salt and pepper to taste. Remove bay leaf. Serve hot.