Herman Miller 670 Base wobbles/comes off  

Herman Miller's phone number
is +1 616 654-3000. Have you called them?
Your chair is out of warranty (doubly so if you aren't the original owner or if you didn't purchase it from an authorized dealer), so you'll have to pay for the replacement bushing, or snap-ring or whatever, that your chair needs... But it can't be THAT expensive.
http://www.hermanmiller.com/DotCom/jsp/contact/contactEmail.jsp

A new base
A new base runs about $350. I've seen a few come up on eBay too.

There was one
A couple days ago, but I think it was just the legs, so it might not have had the part that you're needing.
http://cgi.ebay.com/Herman-Miller-Eames-Lounge-Chair-670-replacement-BAS...

You need a chair base bushing
Ask your HM dealer about this

weird part
my actuall base is fine but the odd part about it is that the piece that is suppose to stay in were the base screws on (metal solid pole) it comes out of the other half, in other words in that ebay pic it has an empty hole, on mine the metal piece comes with the base when i take it off, like its stuck in there, the snap is still on, on the bottom.

These chairs
do seem have structual problems. Many a thread about the 670/671 makes me think I made te right choice to forgo buying one and instead buying my Saarinen original Grasshopper chair and ottoman. It's holding up, nicely.

So, the post has come detached from the spider?
That's a bigger problem than replacing the bushing and snap ring, which are inexpensive, and designed to be easily disassembled. I think the spider (the 4-pronged piece that screws to the wooden shell) is supposed to be press-fit permanently to the post. You'll need to replace that assembly. But as mentioned above, these come up fairly regularly on Ebay. In fact, the bases that show up there usually include the entire assembly... everything below the shell.

A picture
do you have a picture of what the problem is? If there is metal stuck in the hole perhaps the swivel post has sheared? Which sounds like a remarkable feat! Graham Mancha lists the aluminum spider part on his website for Vitra and Moblier Lounge chairs (European make)which shows the swivel shaft attached. Maybe Herman Miller offers it as a replacement part for the American made version.
(edited by DA - no personal attacks please)
http://www.mancha.demon.co.uk/spares.html

FIXED!!!
so i called herman miller, they said that the shaft that was press fit into the spider mount came off completely and has never even been seen before in the history of herman miller, so they sent me a free one even though the chair is not in warranty
so i got the new spider, and everything works fine now, the shaft is a little loose fit in the base of the chair but its better then a broken base

My limited experience
with Herman Miller has never been bad; they are knowledgable and helpful. But, be farewarned; they clean out their warehouse of discontinued product parts when the item is discontinued....HM does not maintain parts for your CSS and other older HM products, alas.

You're
welcome.