Orange Chair with Ottoman  

It looks like a Milo Baughman for James Inc. chair and ottoman. It would be easiest to confirm with a picture of the chair in profile, but perhaps you can google the name and see for yourself.
Yours is missing the original tufting on the back cushion, but when done well they are very sexy chairs!

It does look a lot like the Milo Baughman lounge chair but I think the curve of the top of the arm is a smaller radius than that of the MB chair. Hard to say for sure without an unobstructed side view of the chair, but looks like it to me.
I think also that the orange fabric is original, just based on that odd cardboard dust cover under the chair. It is very unlikely than an upholsterer would be able to remove that and replace it without damage to the edges, nor would he have added something like that with perfect cutouts for the legs and frame bolts. And if it's original, I don't see any signs of button tufting that was removed.
This was a popular style of chair. I'd hang onto it if I were you---if you like it a lot, that is. You can easily get the foam in the seat cushion replaced, as well as whatever is in the back cushion if that needs it too. It's a great color and the fabric looks pretty clean in your photos.

Maybe I should have mentioned that I own these chairs and provided a picture as "proof of identification". With original upholstery including tufting but arm covers removed for their glam shot.