Do you know how to remove rust from steel rod furniture?  

I don't know
how you would remove rust without disturbing paint. The steel is rusting under the paint, surely, with some rust breaking through the paint in pinpoints -- if you look at the surface under magnification. Once rust starts, the paint is toast -- no ?

Non-Acid
Use a rust-remover that does not contain acids.
There are paint-safe removers that will remove the rust and not disturb everything else. After that use a clear coat over the affected area (and areas youd like to prevent) that contains a rust inhibitor.

Thanks for all your help with this.
I am restoring a Clement Meadmore cord chair which has patches of rust under the cord, but I don't want to repaint it and lose it's original character. I just want to remove the rust patches and prevent further rust.
Finding cotton flag line will be a challenge too, but hey, this is what we do when we wanna preserve beautiful mid century furniture.

Thanks,
Tick

Evapo-Rust will do what you...
Evapo-Rust will do what you want, but you'll need to work out a way to immerse your chair in it. Probably best to do one portion at a time in a shallow tub so you can get away with buying just a gallon or so.
Afterward, though, you'll need to coat the exposed metal with something to inhibit further rust formation... So are you SURE you don't just want to repaint the whole thing?
Nautical rope made from cotton is rare, but you should be able to find some somewhere. If you're searching the web, maybe try "signal halyard" instead of "flag line". Or see whether your local hardware store sells braided cotton sash cord that's suitable.

WD40 or RP7 will remove but...
WD40 or RP7 will remove but you will need to etch prime it asap

Rust
White cooking vinegar- rub some on with a cloth leave it 20 mins then wipe it off.

Platner?
Anyone have success removing rust from Platner furniture without having to replate? I've tried a little chrome polish on a rag...no luck. Perhaps steel wool, then keep it waxed?

Chrome?
I always check in with car restoration forums.
If i see something worth a try, i test it in a very small area.
Googled 'removing rust from chrome'
(i did not read thru...just a hint of my process)
http://www.vintagebmx.com/community/index.php?showtopic=4004702&st=0

Thanks everyone
I have quite a few options now. I really appreciate the advice. I had googled this and got a load of suggestions but you really don't want to screw up with vintage furniture.
Thanks Tick.

ive done steel wool before,...
ive done steel wool before, decent job.

Try
Try navel jelly - disolves the rust & leaves a shine - test small area first. rbjr

Thanks for all your suggestions.
Today I spoke to the conservation dept at the Tasmania Museum And Art Gallery and they suggested using rust converter with 0000 steel wool.
Apparently It dries black and is less noticeable. So many options.