Need help with tulip chair cushion  

do you have photos? I'm...
do you have photos? I'm visualizing what you describe, but I need to know that I'm correct. I've never heard of this - but I've also never heard of a straw stuffed tulip cushion. Most cushions I've seen are attached with velcro. Perhaps when someone reupholstered this they did it? If so, there would ne no messing up the vintage integrity of the chair. I'd just go ahead and cut that sucker out.

I know the early Eames bikini...
I know the early Eames bikini pads were stuffed with horsehair, but straw seems so "lumpy" and stiff for such a thin cushion.

Before velcro held the...
Before velcro held the cushion in place, they used a metal circle that was attached to the chair, to hold the cushion on.
The pad is likely held on with a string tied around the circle. So untie the string to free it.
I could be wrong, I have only seen pictures of these older versions. Is your chair a swivel version?

You are correct donsof
The cushion is fabricated with a "drawstring" on the bottom like a hooded sweatshirt. To remove your cushion, lift it up from the bottom and find the string, untie it and give it some slack. You will need to gently pry the string-filled hoop off the ring in the bottom of the seat.
Obviously, you need to do the reverse to re-attach your cushion.
This is only for the first generations tulip chairs. Knoll soon replaced this with a simple velcro attachment.

Thanks, guys!
I can't wait to get home and get that cushion off! Thanks to everyone for their reply. I apologize for not having photos. I'm thinking that once I get it off, I'm going to make my own cusion and attach it with velcro instead of fooling with the drawstring again.
And you're right, the cushion is awfully lumpy. Of course, the straw (or maybe horse hair? hadn't thought of that) is disintegrating and little bits are everywhere in the seat. But for twenty bucks, I'm still considering it a rediculous steal!