Can minors open an account in Illinois - yes. If they can't yet sign their name, well I am not sure how they can enter into such a contract.
(205 ILCS 5/45.1) (from Ch. 17, par. 356)
Sec. 45.1. Accounts for minors. A state bank may accept deposits made by a minor and may open an account in the name of such minor and the rules and regulations of such bank with respect to each such deposit and account shall be as binding upon such minor as if such minor were of full age and legal capacity. The receipt, acquittance or order of payment of such minor on such account or deposit or any part thereof shall be as binding upon such minor as if such minor were of full age and legal capacity.
(Source: Laws 1965, p. 2020.)
The opinions expressed here should not be construed to be those of my employer: PPDocs.com