Not much, unless you buy raw wicker and learn how to wicker.
Here's a guide on how to repair a wicker chair: https://www.wickerliving.com/blog/10-steps-to-repair-missing-or-damaged-wicker-furniture-reed/ I hope that helps!
You can use a strong glue such as gorilla glue to attach any loose ends. If you can get hold of some longer pieces, if that is what you require, then do the same thing by gluing onto the chair. Color it the same shade as the rest of the chair.
A picture might have helped with my reply, but with no other information, I would suggest you go to your nearest craft shop and buy a book on Cane work and some cane of the type your chair is made of. Do not try to use the cane without soaking it overnight in a bath of water to make it supple. Follow the instructions in the book and hopefully you will succeed in achieving a fair repair.
Better still would be to find someone who does Can and Willow Weaving already, could save you a lot of hassle. If you don't want to do either of the suggestions, you could do a patch job to get by, if you use raffia and weave that in and out to secure the ends that have been chewed. Hope that is of some help.