No. As long as you have a valid email address, you can create a Chase QuickPay profile to send and receive money. Simply register your Chase checking account or any US checking or savings account and send money to your recipient. We'll coordinate the direct transfer between banks—without any cost to you.
Note: If you're using a non-Chase checking account for Chase QuickPay, you won't be able to accept payments from other users who also want to send and receive funds using non-Chase accounts. At least one of the accounts in the requested payment (either the sender or the recipient) must be a Chase checking account.
Of course, being a Chase customer has advantages. For example, only Chase customers can use the service to request money from others.