Does anyone know how I can fix this dinning room chair?

Here is an article online about fixing it yourself:

https://www.curbly.com/8483-how-to-fix-a-torn-cane-chair

They DO make the cane backing material these days... I have seen it... try starting with one of the wood working magazines or WoodworkersSource.com. Some upholstery stores carry it.

Rockler wood working sells cane and caning tools.

http://www.rockler.com/search/go?p=Q&asug=&w=cane

Did you try a local school for the blind? they used to teach this. There are videos on YouTube, its not hard. You buy the back and seats all ready woven, and just apply them to the chair through the holes in the wood after soaking in water.

https://www.youtube.com/watch?v=X4Kty28n2wc

A furniture refinisher may be able to help you. Also check out someone that repairs wicker. They also sell chair covers if you'd just want to cover up all of your chairs until you can find someone to do the repair.

that type of cane ing might be found a a large roll...you might have to sus out a woodworking / refinishing book. A friend of my family had his own furniture repair shop...he had different styles of caining on display. I do rember him soaking it, applying it damp, and letting it dry to make it taught.

I took a class in caneing. You need to remove not only the woven part but also the strip around the chair that holds the cane in place. Use a dremel to remove any glue residue. You can buy caning in rolls along with the strip that goes in the groove. I forget what it's called. Soak the caneing roll. Stretch it into the groove along with the strip that goes into the groove. Use wood glue to do this. You may have to stain it after it dries.