Just figured out how to do it for my case. I was holding BTC in Bitcoin Core.

I opened up Bitcoin Core -> Help -> Debug Window
In that window in the command line type: dumpprivkey YOURADDRESS
But swap the word YOURADDRESS with your bitcoin wallet address and then hit enter.
Next you will be presented with your private key. Save this some where very secure.

Next download and install http://www.electroncash.org/
When you are installing it will give you the option to restore your wallet using a private key. You simply copy the private key we got in the previous step and paste it in the box.

You finish the install and your balance should show the correct number of BCH coins in Electron Cash Wallet and you should still have your bitcoins BTC in your Bitcoin Core Wallet.