Can a financial institution require a customer to sign up for electronic statements as a condition of opening a deposit account online?

We will be offering online account opening, and would like to require customers to sign up for electronic statements at the time of account opening. We do not require electronic statements for accounts not opened online, and we will allow customers to change to paper statements at any time if they wish.

I did not see this specifically addressed in Reg E.

Yes.

Reg. E allows electronic delivery of its various disclosures, PROVIDED you and each customer have already completed ESIGN's opt-in process.

ESIGN does not prohibit all-electronic business relationships. It does prohibit unilateral demands that existing paper-based customers accept e-documents. The way to handle your account-opening is to first require account applicants to opt in for e-delivery, and then proceed with opening the account. Done in this sequence, you will avoid the problem of customers who open the account and then skip the e-delivery opt-in steps.