Chairs on the Original Star Trek Series?  

Burke Model 115, apparently.
Not to be confused with Burke Model 103, which is close but not exact.
http://www.cloudster.com/Sets&Vehicles/STEnterprise/Burke_Chair/BurkeCha...

yeah, all of those on the...
yeah, all of those on the bridge were burke.
personally, i've always like the 4 star base on these much more than that on saarinen chairs.
http://2.bp.blogspot.com/_YBAthzRXgUo/R_7O0oXzI-I/AAAAAAAAALU/tfNhf05fJB...

Star Trek TOS chairs...
Bridge station chairs: Burke model 115
Briefing Room 'arm' chairs: Burke model 116
Command Chair: Madison
Burke chairs were made in Dallas, TX, and were knock-offs of the Knoll "Tulip Chair" designed by Finnish American architect and designer Eero Saarinen. You may have seen his "Gateway Arch" in St. Louis?
The bridge station chairs were Burke model 115 chairs painted a light-blue color (sometimes referred to as VW-bus blue - they look off-white on screen because of the intense lighting). The chair fabric was a pebbled black vinyl for both the cushions, and chair backs. Three custom triangles were affixed to the lower chair back. The 'lip' on the upper back and upper sides of the chair was trimmed off to allow for the slip-on 10-inch chairback extension. Several websites detail the DIY Burke to Trek chair conversion.
The briefing room, and captain's quarters 'dress' chair were Burke model 116 with molded 'arms'. All were painted light blue. The dress chair was covered in a red/gold checked pattern also seen in the beds and sheets. In the first season, the chair bases were painted BLACK, for the 2nd and 3rd seasons, the bases were changed to a less reflective CHARCOAL/DARK GREY.
The Captain's Command Chair is based on the Madison swivel base office chair - the single chairs are VERY rare, however, some are still found in older dentist & doctor's offices - there was a 3-seat sofa design that is more common than the single seat chair. See the photo on trekbbs for more info.