I use them for making pork and chive dumplings and for the usual dipping sauce that goes with them (water, soy sauce, sugar, rice vinegar, sesame oil, a bit of red pepper, and chives).
You can also use them pretty much anywhere you would use the green portion of green onions.
The challenge is to find a way to use up the whole bunch, which is HUGE at my market.
Chinese chives are actually garlic chives. They have a mild garlic flavor and can be used as you would a small amount of regular garlic. Rinse very well, chop in small rounds and add a few tablespoons to a sauté, or a pinch here and there where you want a hint of garlic...salad dressings, marinades, diping sauces, etc. They are very easy to grow in a home garden and reseed after flowering a lovely white flower in mid to late August. I've had a patch in my garden for more than 15 years!