Gluten, a protein in wheat, barley, and rye, gives bread its chewy texture and structure. Though harmless for most people, it has become a target of dietary trends, fueling. No, gluten free is not hyphenated.
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The temptation is to throw in extra hyphens just in case, e.g.
Therefore, a hyphen is needed to group the modifiers together so you know the recipe has no gluten.
The gluten free vitamin rich bread is good for you. But nobody would be correct in. Scientists say there is not enough. Does gluten free need a hyphen?
As for hyphenating, i'm seeing it both ways. Not containing gluten (= a sticky substance found in some grains, especially wheat) we sell a range of gluten. Containing no gluten (= a protein contained in wheat and some other grains): Gluten free means a food does not contain any gluten, which is a protein found in wheat, rye and barley.

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For consistency's sake, though, you might as well hyphenate it when. Containing no gluten (= a protein contained in wheat and some other grains):



