"Заморить червячка" is an idiom which can be loosely translated as "to get a bite to eat", or "to have a snack / to have something to eat".
Which worm does the expression refer to? What is its origin?
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The phrase is French in origin ("tuer le ver") and referred originally to the drinking of alcohol on an empty stomach. This was supposed to quite literally "kill the worm" of the parasitic variety.
Here is a link to the French Wiktionary.