Parent-chapter relationships are among the most difficult to control.  The first question is whether the chapters are separately organized as separate entities, or whether they are merely chapters (or divisions) of the national organization.  If they are merely parts of the national and not separate entities, they can use your EIN and are covered by your exemption.  But you are totally responsible for everything they do, or don’t do.  They are you, and their liability is your liability.

On the other hand, if they are separately organized as separate entities, you are not directly responsible for their activities, but they do not qualify under your exempt status unless you have filed for a group exemption and list them annually with the IRS.  If they are separate, they have to obtain their own EIN, and without a group exemption, they have to apply for and obtain their own exempt status. 

You probably have the relationship written up somewhere, but if you don’t, you should do so as soon as possible.  It is particularly important to protect your name by having the power to prohibit anyone from using it who does not meet your standards.