I would say minimal 3/8" of glass, and I would probably lay a decent weight cloth in the mold, then build it up with mat or fabmat / woven roven (roven and mat stitched together for both strength and density / thickness). But the sphere is one of, if not the strongest, form when fiberglass is used. Glass gets its strength from corners and well its one continuous radius...
I would tell you how I would do it, but um its not that difficult and it took me a whole 5 mins of thinking about it

A reverse way of how I would do it though and how others do spheres is by use of a beach ball. Inflate, wrap, deflate (or cut thus deflating), remove ball, finish. But this would require alot of finishing.
Also I saw a few replicas where plastic, thus formed in a mold, and not hard to punch alot of shells out. Cant really see the 1995$ price I saw on one though!!! I saw a real original go for slightly more. Also when plastic the finish can be perfect, but for glass one would want a nice gelcoat on it.
Hmmmm I think I may make one.... The glass will be pretty hefty though but I had ideas of speakers (like original in the stereo chair) and the use of mini halogens for reading lights, and also a recessed (in the back / top) decent sized lcd monitor exposed and slid into place with some linear actuators
Hmmm I knew nothing of these a few mins ago... I need a job, so I can buy glass to make these and sell them at reduced prices and saturate the market muhahaha. I can see it know, where punching in ball chair in ebay produced as many hits as punching in JDM in ebay motors...