Several questions come to mind, but most importantly, where was it manufactured?
The chair frame is probably rattan (similar to bamboo) and it could even have received some other chemical coatings to protect it. There are labeling requirements which require that fire retardants be identified. You find them in lots of furnishings but especially those made with foam (such as mattresses).
You may want to purchase a new cover for your papasan chair by researching a source that uses non-chemical covers.
For more information:
To learn more about flame retardants in furniture, read Mary Cordaro's "Do BFRs (brominated flame retardants) offgas or persist in upholstery? Would they be in the stuffing of a sofa, or in the fabric cover?"