Children's Hope Act of 2013 - Amends the Internal Revenue Code to allow a tax credit of up to $100 ($200 for joint returns) for charitable contributions to an education investment organization that disburses 90% of its contributions to provide grants to students for elementary and secondary education expenses, if at least 50% of such disbursements go to students who qualify for free or reduced-cost school lunches. Requires a taxpayer claiming such credit, as a condition of eligibility to receive it, to first claim a state qualified scholarship tax credit.