Questions regarding shipping a chair  

You have to use a commercial...
You have to use a commercial freight carrier. I use DHL, but you need to have an account with them. Fedex & UPS both will do air freight, but it's signifigantly (5x) more than ocean freight.
Another option is to use a freight forwarding company. They are not actually the carrier, but more of a logistics company. They will get you in as an ltl shipment. Going with this option will help you get items through customs. I have used a company in the past called Estes Express as a freight forwarder from Japan.
About customs. What ever you do, DONT use ANY solid wood in the construction of the crate. Use only plywood/mdf/osb, otherwise you run the risk of your lovely chair being incinerated without notice.
Hope this helps.

If you're talking about an armshell...
It's tricky. Considering the size limits, there's not alot of clearance in the box to protect the shell. If you haven't done it before, I don't know that I'd suggest it. Maybe just stick with domestic shipping. Or you could pay someone to do it for you. But that gets expensive.

i ship armshells all over ...
i ship armshells all over the world . don't worry a bout under packing them they are indestructible!! . cost 60 dollars to London

It's tricky but possible.
You will need to build a custom box to fit the shell perfectly in order to meet the USPS size limit.

thanks
After reading these replies I am leaning toward sticking to domestic shipping. Last thing I need is an email from the purchaser stating it arrived damaged.
I really appreciate your input. Thanks.

I had 2 upholstered...
I had 2 upholstered armshells shipped to me from the US via USPS, in one package. They were packed very tightly but it's possible. It cost about 80$.

claus
Were they just in a regular cardboard box? or was there some type of elaborate internal structure to keep it rigid?

it was just a regular...
it was just a regular cardbox, it just wasn't exactly square. It "adopted" to the shells' shape and had a bump as the backrest stood out a little. As LRF said: these shells are quite indestructible and they arrived without damage. It's a matter of tight packaging to meet the size restrictions. If you want to ship a base/ bases as well you might need a second box though.
With DHL I even shipped an aluminum group lounge chair once, the maximum size for a package is 120x60x60cm which is good enough for most chairs if you are willing to disassemble them. But then again here in Germany you don't need need a special account to use DHL.
hope I could help...