ODESSA, Ukraine—A man in a baseball cap walked into a crowded office here and picked up a Babolat racket bag. But he wasn't going to play tennis. Inside the bag was a concealed hunting rifle.

"I hope to God I'll never have to use it, but it's a restraining factor," said the Ukrainian military veteran, a businessman in civilian life, who has joined this city's grass-roots movement to resist the pro-Russia separatist threat.

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