Snip flowers and stalks no closer than 3 or 4 inches to the bottom of the plant and they should keep regrowing like weeds all summer.
Chives also reproduce well; to propagate at the end of the summer just gently dig up a cluster and separate into individual bulbs, then plant about 8" apart in a new pot.
The entire chive plant is edible - the clustered pompoms can be picked apart into their individual flowerets and scattered in salads. The flowers are funny; they smell fragrant, like a wildflower, but also faintly of garlic and scallions!
It's actually best to remove the flowers frequently, since this will help the bulbs (also edible) to produce more freely. The primary edible part of the chives, though, are the long stalks, which are great snipped into salads and other dishes. They shouldn't be cooked; they're too delicate for that.
Chives are one of the hardiest, easiest to grow herbs in most of the Midwest and Northern zones, as well as most of California. Give them a try for their pretty flowers and delicious flavor.
(Images: Faith Hopler)