Images via Traditional Homes.
The fabric on this chair is from F Schumacher--it's a little expensive, let us warn you. Fortunately for a small chair like this you should only need 3-4 yards. The pattern is called Gordian Weave and it comes in three different colorways. It is a little bumpy though, as the knot pattern is raised quite high.
You can find it in our F Schumacher fabric section.