Forget Antiques Roadshow. I have all the books and I know how to use them. DO NOT CLEAN IT. You have hit a home run. This is called a slat back, rush seat rocking chair. It would not have a maker's mark on it. The rockers themselves are made of either oak or American Chestnut due to the grain that I can see. Appears to be oak. The "rush" is bull rushes, from a swamp! Yeah, those kind! It is held together by wooden pegs, correct for it's period. It has a utilitarian design. That said, I'd say the chair was made - don't have anything in your mouth or you'll choke - ca 1750 -1800. It could be either a littler earlier or later, but that is the general range. It should be worth hundreds, at least, UNLESS you clean it. If you clean it you will ruin the value. Well done. I have numerous similar types at home. My earliest piece of furniture is an American cherry tilt top Queen Anne candle stand. Top is about 15" in diameter. It came out of Boston. Made ca 1720's.