Put the onion, carrots, celery, thyme, parsley, chicken broth, and water in a medium pot. Season with salt and pepper to taste, and bring to a simmer over medium high heat. Simmer until the vegetables are almost tender, about 5 minutes.
Add the noodles and cook until tender, 5 to 8 minutes (depending upon the size of the noodles). Add the chicken, warm through, and then adjust the seasoning if necessary with salt and pepper. Serve garnished with parsley and dill.
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