Garlic chives can be chopped and used as a garnish just like regular chives are; try using them in compound butter or sprinkling on soup. They can also be treated more like a vegetable -- try stir frying or stuffing them into dumplings. Garlic chives also pair well with eggs; try using them in a no-flour-needed egg noodle.
However you decide to cook with them, do it within a week or so. The longer they're stored, the more their flavor will intensify.