Can I claim my BCH if my BTC is held with Coinbase? I have BTC in an account with Coinbase.

Since Coinbase doesn't support BCH, they don't provide access to it.

In all honesty I don't know much about bitcoin and how to move my BTC from Coinbase to an offline wallet, so when I received the notification they wouldn't support the split, I didn't understand the ramifications.

From the little I understand at this point, I believe this is the situation I find myself in, and I am looking for verification that my points below are correct - hence this question:


Coinbase owns the private key to my wallet with them.
If I now move my BTC to a different wallet, to which I own the private key, only the BTC will be moved.
As such, the BCH (which is technically mine), is held against the private key in my Coinbase wallet, and won't be moved.
Therefore, to all intents and purposes, unless Coinbase is somehow persuaded to release the BCH and/or private keys to their BTC customers, that BCH is lost to me.


Final question:

Is there any way for me to obtain access to my BCH?
If you didn't move out your BTC before the fork, then your BitCoin Cash tokens remain with CoinBase. They are not really lost, but they might remain in their system for a while. Here is the explanation directly from CoinBase Support:


  We are planning to have support for bitcoin cash by January 1, 2018, assuming no additional risks emerge during that time.
  
  Once supported, customers will be able to withdraw bitcoin cash. We'll make a determination at a later date about adding trading support. In the meantime, customer bitcoin cash will remain safely stored on Coinbase.
  
  Thank you,
  
  Coinbase Team