I'm assuming you're talking about the normal wooden chair. At level 10 you have access to the Furniture Store, which you must buy. Once you buy the Furniture Store, you can build a chair with the components listed (2x wood, 1x screws from the Building Supply Store, and 1x hammer from the Hardware Store).
There's also the Garden Furniture, which looks like a chair in the picture, but that's not until much later.
