If you have a Bitcoin (BTC) balance on Bittrex during the BCC UAHF time on August 1st, 5:20am PT (12:20pm UTC), you will be additionally credited the equivalent amount of Bitcoin Cash (BCC) on a 1:1 basis. i.e. 1 BTC on Bittrex held during the on-exchange snapshot will get you 1 BCC. BTC held on orders will also be credited. Only the BTC held on your account is eligible for BCC. Full details below.
Bitcoin Cash (BCC) is a proposed digital asset based on the Bitcoin ABC client. BCC is set to perform a User Activated Hard Fork (UAHF) from the Bitcoin network on August 1st, 5:20am PT (12:20pm UTC). BCC includes some code and consensus changes such as SIGHASH_FORKID replay protection, support for 8 MB block sizes, modified difficulty adjustment and removed support for Segregated Witness.
At this time, several exchanges have expressed the future support for BCC trading as well as mining pools. Bittrex will be monitoring this situation closely. Bittrex will close deposits and withdrawals of Bitcoin (including 2nd layer protocol XCP/OMNI and associated assets) 24 hours prior to the BCC UAHF time on August 1st, 5:20am PT (12:20pm UTC). The wallet will remain closed until the majority hash power chain is clearly established. Trading will remain active during this time. In the event of a chain split, Bittrex will take all reasonable steps to ensure that customer funds can be preserved on both chains.
Bittrex will monitor the BCC network stability and developments and assess the viability of opening trading of BCC assets. There is no guarantee that any markets will open to allow BCC assets to be tradable on Bittrex exchange. In the case of no BCC market opening you will be able to withdraw BCC.
Bitcoin Cash Bitcointalk ANN thread
Bitcoin Cash: What You Need to Know
Update 1: Changed term "credited" to "additionally credited". Changed term "network" to "network stability." Added "In the case of no BCC market opening you will be able to withdraw BCC."
Update 2: Add "PT" timezone for clarity.