It depends on whom you ask.
Most experts in celiac disease have concluded that distilled alcoholic beverages made from gluten grains including whiskey, commonly made from barley are gluten-free to the U.S. Food and Drug Administration's proposed standard of less than 20 parts per million, because distillation removes the harmful gluten proteins.
In fact, the National Institutes of Health's Celiac Disease Awareness Campaign advises that cocktails made with distilled alcohol are safe for celiacs to drink.
However, not everyone agrees. The Celiac Sprue Association does not recommend any form of Scotch or whiskey; instead, it advises those following the gluten-free diet to stick with potato vodkas, rum and tequila, all of which are made from non-gluten grain sources.
Some people with celiac or gluten sensitivity can handle drinking Scotch or whiskey without any problems. However, others (me included) experience severe gluten reactions if we consume something distilled from gluten grains.
It's possible that distillation doesn't remove 100% of the gluten (studies have been mixed on this point), or that a small amount of gluten is added back in as part of processing after distillation. In some cases, whiskey manufacturers add caramel coloring (which may contain gluten) or even a small amount of the undistilled grain mash after the distilling process.
So should you consume whiskey as part of your gluten-free diet? I'd advise going slowly, especially if you're particularly sensitive. You may find that you tolerate it just fine, but you also may find you react. If you do react, try potato vodka or unflavored rum instead.
There is one other option for those who can't handle whiskey distilled from gluten grains: Queen Jennie Whiskey, crafted by Old Sugar Distillery in Madison, Wis. Queen Jennie is made entirely from sorghum in a facility that does not use wheat, barley or rye, according to Old Sugar owner Nathan Greenawalt.