Babylonians/Sumerian/Metsopatamian culture - birthplace of Western Civ definitely is the most deserving.
China may have a lot of achievements to its name but they opted to shut out the rest of the world and actually let people rise to leadership in their country with the intent of destroying their culture! I think, for a country to be great, they should be able to preserve their culture no matter what. Note: I am NOT stating this is the only requirement and I am not going to argue about my view on it. Just saying this because of all the anti-Civ debates here because of other people's views on what a civ is.
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