Poison Ivy Oils on Furniture from Pet?

I am wondering if my dog or cat got into poison Ivy and laid on a chair, if the oils are in the fabric of this chair, how would I go about removing them? Can I use my hoover steam cleaner on the chair, and if I do will it remove the oils or should I pre-treat it with something before?

I have a small but quite irritating case of pi and that is the only way I can think of I possibly got it because after sitting on the chair and watching a movie, I started itching and the subsequent red patches starting showing up. Any help on how to clean that chair would be greatly appreciated!