If your chapter is incorporated, you would need an Employee Identification Number and certificate of incorporation.
If your chapter is NOT incorporated, you would need a Social Security Number or Individual Taxpayer Identification Number (ITIN) of one or two of your officers.
A charter, articles of organization, or similar legal document that shows when your chapter was formed. A charter or other official document that lists the officers of your organization.
The bylaws must provide a clear summary of the purpose of the non-profit organization. Bylaws must name the board members, and those who will be responsible for the bank account. The bylaws should stipulate not only the goal of the non-profit organization, but also the board policies.
Chapters should be aware of chapter's cashflow and whether or not you will be able to meet the minimum deposit in opening a bank account, and the minimum balance in the account.
Check with your bank on annual fees, transaction fees, and any other fees that might be incurred.
Chapters should have a policy on managing the bank account, which includes check signing procedures, bookkeeping, succession process.
Most national banks will have an account specific to nonprofit organizations, but you might want to consider looking into credit unions, and smaller local banks and see if they have any nonprofit discounts.