Susie,
as far as I know, it would be best to wait until the new chive plant is well established before regular use, so I'd wait until the end of this growing season, maybe even next year, before chopping off chunks!
Rosemary, the little buds you mention are probably the flower heads! As Mimi says, they are very pretty! Probably can collect seed from them too.
sallylockhart, if you wanted to transplant them, the sooner the better. Well established chive plants are generally very hardy and so moving them now should be ok.
I am, of course, pretty sure I'll be corrected on some of this as the day goes on! As for myself, I will probably try sowing more seed or keeping an eye out for a chive plant in one of the supermarkets. I bought a bay from a supermarket, planted it up and it seems to be doing well!
Niamh