LCW-whose is it?  

Hi Holly
This is a Lounge Chair Wood (LCW). It was designed by Charles and Ray Eames in 1945-46 and produced from then until 1957. It was re-introduced in 1994 and is still in production today.
The manufacturer is Herman Miller of Zeeland Michigan. Usually the chairs have a paper or foil label on the underside to indicate the maker. The fact that yours is incised with LCW indicates that it is from the first production. It is most likely from somewhere in the 50's because the pattern of screws on the bottom is 5-2-4, not 5-2-5, which would indicate a very early production date.
It looks like its in good condition. I cant tell if the wood is veneered in walnut or mahogany. Many different types of veneers were used over the years. Mahogany was specific to 1951 (I think-correct me if I'm wrong) where-as walnut has been in production from the very beginning.
Charles and Ray Eames (husband and wife) are considered to be one of the most influential design forces of the 20th century. Many many volumes have been written about them - for a brief overview you can check out the Design Index on this very site.
The chair is fairly valuable as a collectors piece - especially the earlier productions. You're quite lucky to find one in such good shape! Some more brief information in the link below.
I hope this answers your questions!
http://en.wikipedia.org/wiki/Eames_Lounge_Chair_Wood_%28LCW%29

thanks for the answer
Thanks for your very complete answer. I was familiar with the chair (from books) but had never seen the inscribed LCW or the patent label. I have 3 more (!), in varying states--some water marks/scratches. To refinish or not is the next question. Thanks again-love this forum

At last resort
Holly- lucky find! This is my favorite chair of all time 🙂
I'm very preferential to a nice patina of age - that is, accepting that the chair is an antique and accepting the wear and tear it has suffered along the way. I believe the Japanese call this Wabi-Sabi (again, someone correct me if I am wrong)
By refinishing the chair you are basicall erasing its history - in which case, why not buy a new chair?
Of course, if a chair has suffered so much damage as to not be usable I would suggest doing as much restoration as possible.
http://en.wikipedia.org/wiki/Wabi_sabi

If
I wanted to add this part on, but it slipped my mind in the last post.
There are a few different options you have to try hiding/minimizing the marks before you require a full-on refinishing.
A number of "potions" exist in your local hardware store to cover up water marks and small nicks or scratches. My personal preference is to slap a coat of pastewax on and buff the heck out of it. 🙂
If you do go for the complete refinish I would talk to a furniture refinisher about the least destructive methods of doing it.

lucifersum is right on this one
Although i do not always agree with every thing luifersum saya i do agree
By refinishing the chair you are basically erasing its history - in which case, why not buy a new chair?
Unless they are all crapped out and we can not see on the pictures i would leave the chair a lone,
it has been pretty much established that you have one of the early day originals so be proud and don't do a thing buy a new one in a color if you want to be different i have one in yellow and love it...

won't refinish
LRF, you and lucifersum have me convinced. There is only 1 of the 4 that would really benefit from the removal of a rather large watermark--I'll give the paste wax a try.
I really am pleased to learn that they are early ones, and to think that I found them in a garage sale....