They shouldn't spread too much - unless you allow them to seed. Clip off the flower buds when they first appear, or immediately after the flowers begin to fade... and throw them outside of your garden to be on the safe side.

Fully opened flowers make the most beautiful bright pink vinegar. I would not throw them out.

You can also use them in salads, they add a nice onion-y flavor.

In my experience, it is not difficult to keep them from spreading. They do form a pretty big clump if left to their own devices, but it has never ever been a problem for me. (unlike the "wild onions" which grow here and are impossible to get rid of, I have not made this mistake, but know of other who have.)

I've had chives in the same clay pot for ten years. We make good use of them during the growing season. (So delicious with potato salad or scrambled eggs!) Every year they come back but don't seem to spread all that much: Very compact. Mine get a mix of sun and shade, so that may be a factor. Since I cut them regularly, I rarely see flowers.

still_kris: I remember the "wild onions" from my childhood in NJ. We kids would chew on them and then breathe onion breath on each other. :D

Thanks for responding, everyone. I was worried because in some earlier incarnation of my garden, I think I had something called garlic chives or, maybe it was those onions. They were really hard to get rid of.

I guess the trick is harvesting the blooms for enjoyment without cutting off the usable surrounding chives.

Garlic chives are different from regular chives and can be really invasive. Regular chives are much tamer and easier to control. The real key to either of them is not to let the flowers mature enough to set seed then they both tend to grow tight clumps.

Mine have always behaved themselves. :)

My garlic chives do not behave themselves because I always let them bloom and self-seed so now I have garlic chive seedlings in my brick walkway. They don't clump as quickly as chives do.

I also don't cook with them as much as I go regular chives.