Both ETH and ETC have same address schema and fully compatible. If you by mistake transferred coins to an address that belongs to ETH wallet, you can recover it if you have access to Private Key to address in ETH.
To claim your coins you need to export your ETH Private Key from ETH wallet and import into a ETC wallet. Most of the wallet provide you a Private Key for your address. If you use a third-party hosted wallet, or an address provided by exchange, you'll need to contact their support to get your Private Key for ETH address.
After receiving your Private Key for ETH address, you can import it into a ETC wallet, such as MyEtherWallet or Emerald Wallet to get access to your coins on ETC chain.