A few nights from now the Chaldean archbishop of Erbil, Bashar Matti Warda, will celebrate Midnight Mass with his Iraqi flock. The faithful will walk into their cathedral through a passageway modeled on the Ishtar Gate that was the main entryway into ancient Babylon under Nebuchadnezzar II 2,600 years ago. Once inside they will celebrate their Christmas liturgy in a dialect of Aramaic, the language Jesus spoke.

This year, Erbil is a microcosm of the hopes and anxieties of Iraq’s dwindling Christian population. Once a small...