My first thought when I saw it was that this must just be a prop sitting around the studio that they just grabbed as another oddity to fill Joey's flat with. Especially since it was used in first season episode "Haven" of ST:TNG as alien space ship filler. Now, here comes the strange part, "Haven" was first aired in October of 1990 and "The One That Could Have Been: Part 2" aired February of 2000 that's a nearly ten year gap where this odd piece of furniture hasn't shown it's face. I suppose that isn't the strangest thing that could happen, I mean you see old sci-fi props shared between films all the time over longer time spans (although usually with a little more frequency) so I thought I would have little further dig and found out that ST:TNG filmed on the Paramount Studios stages 8 and 9 where as Friends was filmed at The Warner Bros. Sound Stage 24. So, I am not 100% on how props are shared between studios but I imagine that unless they share a single prop supplier these might be two separate chairs!

So, a little more googling and I have learned that this type of chair was actually a designed in the 1980's by a Norwegian furniture designer named Peter Obsvik it is the "Garden" chair. Here is his page describing it from his site. The version on his site here looks like the original design and is what we have seen in ST:TNG and Friends. Oddly it seems the original use of this furniture was as flexible outdoor seating. The newer ones you can find on his site look like they are from a 2011 relaunch of the design which look less scifi but at least a little bit more comfortable.

I was hoping to end this article with a link to where to find the chair if you for some reason wanted one but it looks like they were only being sold by a Norwegian company called Rybo and there website looks to be broken at the moment. So instead I am going to leave you with a collection of these interesting looking chairs.

EDIT: I found that you can get simpler versions of this chair over at http://www.globeconcept.org/ not quite the same, but it is a start!