At this point you *might* be able to get a Pi Zero, but it does not look like the C.H.I.P is available for mainstream purchasing now.
All things considered though, I'd go with the Pi Zero for now, it has a very large community and much better support for it, and it does not need an HDMI addon in order to plug it into a computer monitor (fewer and fewer displays have composite these days). Full disclosure though, I own 3 Pi2 boards.
What really annoys me about both of these is that the cost everyone is focusing on ($9 and $5) is very misleading. Once you buy the stuff you need to actually work with them, the both come in right around $25 (as per the article, C.H.I.P + USB cable + HDMI addon = $23, Pi Zero + USB cables, HDMI adapter/cable + storage = $25), which 3 to 5 times the quoted cost, not a lot of money but still not as cheap as they lead you to believe.
What I would have loved to see was them sacrifice a bit of space in order to put on a single regular USB port and regular HDMI port on the Pi Zero, even if this meant it was a bit bigger and even a buck or two more.
EDIT: C.H.I.P's website is here:
http://getchip.com/pages/chip You can pre-order them, and they estimate it will ship in June of next year. Also, if you want to add the HDMI addon and an HDMI cable, that $9 computer will cost you $30 on their website, VGA would save you $5 off of that. I dunno, these to PC boards really feel like bad manipulative advertising to me. "Come get a computer for $9! O you want one, well in order to actually use it you'll need these accessories that cost nearly twice as much as the computer does." Just rubs me the wrong way I guess.