It's not Chicken either, because of the reason you just gave.

Edit: Seeing how this post got downvoted with no reply being posted, I have to assume it was someone who doesn't know much about game theory, so let me explain:

If the terrorists gain no extra value from killing a hostage if the government pays, then DC > CC is false for the terrorist side; however both PD and Chicken are symmetrical problems that require DC > CC to be true for all sides. Therefore, this problem is neither PD nor Chicken.