In a slow cooker, combine chicken, onion, carrots, celery, garlic, thyme, rosemary, and bay leaf; generously season with salt and pepper. Pour in broth.
Cover and cook on Low, 6 to 8 hours. Remove chicken from slow cooker and shred with 2 forks. Discard herbs and bay leaf. Return chicken to slow cooker and add egg noodles.
Cover and cook on Low until noodles are al dente, 20 to 30 minutes.
