Can you place a hold on a deposit account, if that customer is late on their credit card payments?

No.

Regulation Z prohibits the use of offset for credit card accounts ( §226.12(d) )

The same section allows you to go after the funds in other ways, such as consensual security interest, attachment, etc. But offset is verboten.

Thank you for your help.

Is this something that can be amdended contractually with the customer? We just got this wording straight from our Corporate Counsel when we were working on updating our Master Account Agreement:

"You agree that if you become indebted to us for any reason, including but not limited to our extending credit to you in connection with a transaction you initiate using a bank-issued plastic card, and you fail to pay what you owe us consistent with your agreements with us or upon our lawful written demand, we can take funds from any account in which you have an ownership interest, without notice to you, to pay all or part of your debt to us. This right applies even to loans or lines of credit that are otherwise designated “signature” or “unsecured”."

That seems to indicate that we can offset for credit cards, too... Or am I reading that wrong?

We have the same type of verbiage in our VISA Disclosure, but I think that REG. Z, when talking about a written, consenual agreement, is refering to something like a share secured loan agreement, not print buried in a disclosure.
Our regulatory audits, however, have found no objection with the language in or disclosure.
I too, would be interested to know if ths type of thing has been challenged.

If someone had a credit card with First USA, and they defaulted, would Bank One have the right of offset on the First USA card?

What about if the card is now a Bank One credit card, but was formerly a First USA card?

Debit one card to pay another. I don't see how. Reg. Z wants to be specific about setoffs and I'd be weary of doing this without the blessing of those who will defend the actions.

Just because your Corporate Counsel wrote it does not mean it complies with the law. Show this to your corporate counsel:

226.12 Special credit card provisions.

(d) Offsets by card issuer prohibited. (1) A card issuer may not take any action, either before or after termination of credit card privileges, to offset a cardholder's indebtedness arising from a consumer credit transaction under the relevant credit card plan against funds of the cardholder held on deposit with the card issuer.
(2) This paragraph does not alter or affect the right of a card issuer acting under state or Federal law to do any of the following with regard to funds of a cardholder held on deposit with the card issuer if the same procedure is constitutionally available to creditors generally: obtain or enforce a consensual security interest in the funds; attach or otherwise levy upon the funds; or obtain or enforce a court order relating to the funds.
(3) This paragraph does not prohibit a plan, if authorized in writing by the cardholder, under which the card issuer may periodically deduct all or part of the cardholder's credit card debt from a deposit account held with the card issuer (subject to the limitations in Sec. 226.13(d)(1)).

You cannot exercise offset unless the account is specifically identified as securing the card, unless you go to court and obtain a judgment or levy against the account.