La Chaise?????  

My guess
My guess would be two things:
1. Vitra knows that the sales of La Chaise will be infinitely smaller than sales of the shell chairs - and so they are comfortable making it in fiber.
2. the La Chaise shell needs to be assembled in two parts, which are glued together and then painted. I don't know much about plastics (happily corrected here) but I would guess that there needs to be a certain amount of rigidity in the shell in order to keep the paint from popping off.

I don't know the answer
but I can tell you that La Chaise could not be made out of simple plastic due to its size./
When Knoll replace the fiberglass material on the Womb chair, they tried to test if they could bring back the discontinued Settee. Their experiments proved that the Settee could not be made without the original fiberglass material, which they decided they would not use anymore.

Or perhaps their ecological c...
Or perhaps their ecological concerns just were not the ONLY reason behind their decision to switch from fiberglass shells to plastic in the first place (insert roll-eyes emoticon here)...I mean, considering the current list price of Vitra La Chaise there's still some profit to be made even in fiberglass...

I think....
J.J. is right in assuming that there are other considerations. The injection moulding of shells, any seat shell that is, requires either very substantial quantities or a very high portion of mould amortisation per chair. On top of that the mould for the "Lachaise" chair would be both much more expensive that a regular chair and would require a very high tonnage (clamping force and plasticization capacity) injection moulding machine. The clamping force is in function of the projected surface. I have not compared both but the "Lachaise" is probably between 3 and 4 times larger in projected surface. I would also want to confirm that it is indeed extremely difficult to paint polypropylene (the plastic material used for the shells) As far as price is concerned there is of course no comparison. The polypropylene shells cost probably between $3,75 and $4,50 a piece to produce, depending on the fluctuating material costs. To that one has to add the write-off of a $135.000 injection mould.
By the way, some progress has been done in the recycling of glass fibre re-enforced polyester. Some manufacturers now claim that it is a recyclable material...doubtful still, as long as the re-cycling is only available in very few places...

That Eames Chaise probably has
to be made 'just so'. It's not anything I would ever want, but it's clearly an item that each one has to be hand-assembled. Remember, the shell is made of two independent layers with vericulite in the middle. And those rods have to be super strong and rigid.
Of course, I'm always shocked at the prices these companies charge, but I bet that the La Chaise is a darn expensive piece to make.
Now, why Vitra overcharges for the Nelson clocks is a completely different issue.