Because I can’t figure out if ‘chives seed’ or ‘chive seed’ is more correct.
Anyway. Chives aren’t a thing I think too much about saving seed from. It’s a perennial, and I’ve still got a bunch of seed in the fridge from last year. But, it’s just there for the taking! They flower profusely, then the wee seed heads dry up on the plant, and you can easily see the tiny black seeds inside each little flower bud.
It seems ridiculous not to snip a few off and put them aside. I don’t plan to take all of them, I’ll be quite happy if they self-seed around the place, but a little put away won’t hurt at all. At the very least, I’ll have seed to share. Right now I’m just collecting the flower heads in an open container, once they’re all good and dry I’ll do some winnowing. But you can see how the seed is just falling out of the dry flowers and collecting in the bottom of the container already.
Allium (onions and their ilk) seed doesn’t keep very well. You’re going to want to keep it in the fridge and use it within the year. I’ve had older seed than that sprout, but germination does tend to drop off quite remarkably the older the seed is.