Section 145(k) of the Delaware General Corporation Law is quite clear and emphatic about which court may hear actions for indemnification or advancement of expenses:

The Court of Chancery is hereby vested with exclusive jurisdiction to hear and determine all actions for advancement of expenses or indemnification brought under this section or under any bylaw, agreement, vote of stockholders or disinterested directors, or otherwise.  The Court of Chancery may summarily determine a corporation’s obligation to advance expenses (including attorneys’ fees).

Some might understandably read this statute to preclude any other court from deciding any claim for indemnification.  However, as explained by Judge Frank H. Easterbrook:

Nor do we suppose for one second that Delaware set out to contract the scope  of federal jurisdiction. Section 145(k) allocates jurisdiction among Delaware courts.  Delaware maintains separate systems of courts in law and equity.  Claims based on corporate arrangements go to the Court of Chancery rather than to the law courts, where other contracts are litigated. Such an intra-state allocation has no effect on federal litigation, which merged law and equity long ago.

Truck Components v. Beatrice Co., 143 F.3d 1057, 1061-1062 (7th Cir. 1998).

In some cases, it may not be so easy to determine where a claim should be heard. For example, an exclusive forum bylaw might specify the state of incorporation, an employment agreement might provide for arbitration, and an indemnity agreement might specify the courts in the location of the principal executive offices.  It’s even possible that suit could be brought in a state with an applicable employee indemnification statute.