Quoted below is a tweet from myetherwallet :
⚠ After looking into EthZero, we have no clarity as to (1) what the code is (2) who created it (3) if it is properly licensed. Coupled w/ multiple .exe's that are malicious, we recommend NOT INSTALLING NOR USING ANYTHING RELATED TO ETHZERO AS IT PUTS YOUR SYSTEM & ETH AT RISK
I would probably take this announcement serious. There is no point losing your ethereum for the sake of a forked coin. Some of the replies to the tweet also indicated a possibility of phishing, so be careful if you still plan to go ahead to give out your private keys for claiming ETZ