Ole Wanscher 1960 colonial chair  

Straightforward cane replacement. Anybody competent in chair re-caning should be able to handle it.

Was going to post the above.

Caning is generally not particularly unique. If you're concerned ask the caner to make sure they're recreating the same pattern, but it doesn't look dissimilar to any other caning like this.

with only a limited photo, it looks like pre-woven press-in cane to me. The caner would then only need to worry about selecting the correct replacement pattern, not replicating the weave. Unless there is a subframe, which is hidden in this photo, a hand-woven back would show the caning on the backside after passing through the holes in the frame.

A photo from the front would clear this issue up very quickly.