As militants from the so-called Islamic State (IS) advance across Syria and Iraq, the battlefield exploits of a 28-year-old field commander known as Omar al-Shishani—“Omar the Chechen”—have become a prominent narrative in the conflict. Born Tarkhan Batirashvili, the IS fighter is increasingly credited by observers as a superlative tactician who has overcome the group’s disadvantages in size and equipment to score a string of recent victories in Iraq.

Batirashvili is an unlikely war hero for the radical Islamist brigades. Only a few years ago, after serving as a sergeant in the Georgian army during the 2008 war with Russia, Batirashvili was wasting away in a Georgian prison on illegal gun charges that his father claims were trumped up by the government. ...