Jack Lenor Larsen fabric  

I'm guessing it's not, based on the Larsen fabrics I've seen in person---but I could be wrong, of course. The grayed pastel colors don't look like his typical palette and the weave looks a bit heavy.

There are a number of books about him and his designs so maybe getting hold of one or two of them would help.

I am pretty sure someone else asked about this very fabric on some other style of chair in the past 6 months or so, on this board. Or maybe he or she was asking for an ID of the chair itself, with the thought that the fabric was possibly a clue. I did a cursory search but couldn't find it.