Place the cucumber rounds into the water and let infuse in the refrigerator for at least 15 minutes.
Heat a pot over medium heat. Once hot, add the oil followed by the carrots, celery, onion, and garlic. Sauté until the celery begins to soften.
Add the chicken broth, chicken, thyme, salt, and pepper, and bring to a simmer for about 25 minutes, covered with a vented lid.
Add the noodles to the pot and cook with the lid on until tender; refer to the directions on the package for cooking time.
Toast the bread, optionally. Spread with butter.
To Finish the Soup: Taste the soup and adjust the seasoning with salt and pepper. Remove the thyme sprigs.
To Serve: Ladle soup into a bowl. Serve with a side of bread and butter and a glass of cucumber water.