oaklandtom's Profile

If the cane back is machine cane, with a spline holding the cane in place, it should be fairly easy/cheap/quick to replace. You use the new spline (and white household glue) to hold the sheet of machine-made cane in the groove. I've done a couple of seat and backs of chairs for about $20 in supplies each (caningshop.com). If you can see the holes in the chair back that the cane goes through, then it's woven cane (think a round bundle of reed). More difficult and very time consuming since you're going to have to literally weave the back, but still do-able.
If you don't want to tackle it, there might be a weaving store in your area that would do it for you. Be warned that if they have to weave it, it's going to cost $$$.
Also, if you're gonna fix the finish on the chair, I'd start with that before the cane.
Good luck!