Yep. They're far from a 100% solution, but a large fraction of the dust that hits the chain is coming off the front wheel, and a fender can catch lots of it. Similar to dealing with water, the trick is that most fenders on the market don't go low enough to protect the lower run of the chain very well, often even ones that come with mudguards attached.

Anyone who goes this route should exercise the usual caution with fenders: try to aim for 2cm or so of clearance so that stuff picked up by the tire when riding offroad won't be prone to jamming on the fender, and be aware that sticky clumpy stuff like mud and snow can build up underneath them.