President Trump announced “mission accomplished” after Friday night’s missile attack on Syria, and he’s right if his goal was merely to punish Bashar Assad’s use of chemical weapons. But if Mr. Trump also wants to deter Russian and Iranian imperialism, reduce the chances of another Mideast war and keep Syria from producing global terrorists, he needs a more ambitious strategy.

Even narrowly defined, the military strike was valuable in enforcing the longtime taboo against chemical weapons—all the more so after Barack Obama...