In a 5 liter slow cooker, add the celery, carrots, onion, garlic cloves and chicken. Cover with water and mix in salt and black pepper. Cover and cook on low for at least 8 hours.
After 8 hours, strain the slow cooker liquid into a large pot. REMEMBER TO SAVE THE CHICKEN AND VEGETABLES in the slow cooker. Bring the liquid to a boil and stir in spaghetti noodles. Simmer for 10 minutes.
While the pasta is simmering, remove the chicken from the slow cooker. Use two forks to pull the chicken apart.
Pour the spaghetti noodles and liquid back into the slow cooker. Mix the pasta, chicken and vegetables.