I'm thinking it must be China but I've no idea if it was all together as one complete nation as it is today.
You would have to be a lot more specific by what you consider a country to be, and how far back you would be willing to consider for a continuity.
For example, do you consider France to have existed since the Middle Ages, ie would you separate France into the Ancien Regime, the French Republic, the Napoleonic French Empire, etc.? Are these different Frances'? Do you consider the Tsarist, Soviet, and modern federation of Russia to be one continuous 'country'?