For starters, chanterelles are firm, fibrous, and generally free of bugs. Their texture lets you slice them easily, or even pull them apart from top to stem. This means you can make chanterelle chips.
To make chanty chips, slice the mushrooms as thin as you can on a mandoline, then paint them with melted butter or oil, sprinkle with salt, and broil. Keep an eye on them or they will burn. Take them out of the broiler and let them dry in a warm oven or a dehydrator until crisp.

Hank Shaw
When you dry chanterelles their fibrousness gets more pronounced, and the mushrooms get chewy. So chewy that they will need to be cooked an awful long time to avoid that "Hey! I'm gnawing on shoe leather!" feeling you get from a lot of dried mushrooms.
Dried chanterelles keep their flavor and aroma, however, which makes them worth drying nonetheless. Either use them in soups, braises, or other long-cooking methods, or do what professional forager Connie Green does in her new book, The Wild Table—she infuses vodka with dried chanties.
Is this not the coolest thing? The chanterelles were in the jar only a few hours when Holly took this picture—check out that color! Green infuses her mushrooms in the vodka for only one week, after which you strain the liquor through cheesecloth and bottle.
There are some flavor compounds in chanterelles that are alcohol-soluble, so this method makes sense. It is also why you really want to add a little booze to your chanterelles when you cook them in other ways. Cooking is about extracting flavor, and not everything is water-soluble.

Holly A. Heyser
Can't vouch for the flavor of this vodka yet because I haven't yet tried it. But I have high hopes. It smells pretty boozy, yet that apricot-like aroma is still coming through. Will keep you posted...
Obviously the single best way to eat chanterelles is to sauté them in butter. Yes, you can use other fats or oils, but, other than duck fat, I've not yet found another lipid that brings out the flavor of chanterelles quite as well. Again, there are a whole set of flavor compounds in chanties that are fat-soluble, so you will want to extract them with something. My experience says to stick with butter.
What else goes well with chanterelles? Over the years I've come up with a list of chanty-friendly foods, supplemented by some other items listed in that great cooking guide, The Flavor Bible.
• Butter, duck fat, or olive oil
• Chicken, turkey, pheasant, partridge, quail
• Wild boar, rabbit, or lean pork
• Firm white fish, such as halibut or shark
• Winter squash, potatoes, and sweet potatoes
• Light stocks such as chicken, pheasant, rabbit
• White wine, vermouth, gin, dry sherry
• Cream, crème fraiche and cheese, especially dry cheeses
• Bay leaves, thyme, parsley, garlic, chives, saffron
Chanterelles and cream are a natural, and the best expression of that I've come up with was my version of Auguste Escoffier's Velouté Agnès Sorel, a cream of chanterelle soup. It is, as I have said before, sex in a bowl.