add felt to bottom of Eames LCW/DCW chairs?  

The problem of scuffed and scratched floors
is caused by two factors.
Number one is particles of grit becoming embedded in the glide surface and acting as sandpaper every time the furniture moves. This happens with felt, plastic, and even some metals. Though, with metal glides, once the surface becomes scratched and galled, they themselves act as an abrasive.
The other is the relative hardness of the glide surface vs. the flooring finish. Even if the floor is immaculate (which they will never be in my house) the glides will eventually abrade, scuff, or polish the floor somewhat if they are a harder material than the floor. The best approach I've found for metal or plastic glides is to keep them polished as smooth as possible.
You can of course simply stick those self-adhesive "felt" pads to your chairs and replace them periodically as they get compressed and full of particles, but I've found this approach unsatisfactory.
What I've done to some of our wooden furniture was to glue on pieces of shoe sole leather cut a tad smaller than the contact surfaces using liquid hide glue. The hide glue is completely reversible should anyone want to remove them in the future, and an occasional light sanding with fine-grade sandpaper keeps the surfaces clear of embedded grit. After seven or eight years now, they have proved to be durable and have helped immensely to reduce if not eliminate scratching on our oak floors.

never thought of shoe sole leather
that is an interesting option. I'm guessing you can buy shoe sole leather at a cobbler?
I'll be honest, the floor is just laminate and so fairly durable...I'm more worried about not doing any permanent damage to the chair and keeping it quiet...right now with nothing on the bottom of the legs it's a little loud as you sit down which is disconcerting...though probably not doing any real harm.

Various animal protein glues
are regularly used by musem furniture conservators for its ability to be easily reversed without harm to the original surface.
Franklin's Liquid Hide Glue used to be found in virtually any hardware store. Now it's a Titebond product and increasingly hard to find. Too bad.
http://www.titebond.com/product.aspx?id=9e9995b4-08eb-4fc6-8254-c47daa20...

Do it
I put felt pads under my (newer production) LCW for this exact reason. I don't have to worry about scratching the floor or the bottom of the LCW legs. After about six months of use I'll replace them as they become compressed and dirty.

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I use felt, leather, cork or rubber. Adhesives are reversible. A roll of cork is handy and can be cut to size for odd shaped furniture feet.
Felt sheets are good for ceramics cut to size but i never glue those.
Rubber does not hold up that well on glides but the tiny dot ones are good for cabinet doors to buffer the 'slam' sound.
Some of my vintage glides are so rough and grainy as if they were dragged along a gravel road. Best to protect your floors.

Thanks!
Thanks everybody for the input. Sounds like no real damage done by adding the felt so I think I will probably do that, or explore one of the other options like leather or cork. Glad to know I'll be able to use it quietly on my floors.

I have heard that the flayed...
I have heard that the flayed skin of newly born, albino, conjoined triplet, golden-headed langur is the perfect thing to to apply to your chair to protect your floors.

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You must be on holiday.
I'll have some of that. Mark?

is that available at Target
or is that something I'd have to harvest myself?

Yes, at Target in the same se...
Yes, at Target in the same section as the fine Corinthian leather.

Nothing sticks to langur hide.
Except centrifuged white sturgeon bile. And even then only to the flesh side.

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