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They have put out a statement saying outright that if a hard fork occurs, they will not support both blockchains. If you control private keys on one blockchain and a fork occurs, those private keys control the bitcoin on both blockchains, separately. By stating that coinbase won't support both chains, they are effectively saying that they will decide which chain you will have access too. What will they do with their access to the other chain? I do not know, that is left to speculation. All I care about is that if a hard fork occurs, I am in control of my bitcoins on both blockchains.