I just use a seam ripper after pressing the chain. It seems pretty easy but everyone has a different way

I watch Donna Jordan on her videos and she has a little pair of clippers that she uses and I would love to know what the clippers are called. They look so easy to use.

I forgot to add that my friend has one of those items that sit on a table and you can clip threads and her complaint about it is that it is not stable and tips over all the time when she is trying to clip threads after chain stitching. Just a thought for you to consider

Eleanor Burns uses that gadget to separate her chained pieces... but she makes everything look fast! I like to snip them apart with my scissors, because I can trim that little triangle of seam allowance sticking out at the same time.

If you own a needle threader, it has a cutter on the top.

I have been reading the responses and wanted to add:
I made this quilt for my son, and it was all 2.5" squares. I chain pieced most of it and believe me there was a LOT of clipping to do. Had I not had my handy cutter, made by my son, I would not have been able to do this. My arm and hand would have given out way before the need to clip did. I made 9 patches from the squares then sewed the 9P together to make larger sections. It is a queen size quilt. Now you see why I needed my chain cutter. lol[ATTACH=CONFIG]603203[/ATTACH]
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At sewday yesterday, someone had the ripper stuck in a holder. She was using it and yep, impaled the side of her hand. It does happen.