This chair design is as simple as it gets: a few cuts from a single 8x12 board and you've got a comfortable seat with a solid backrest that can be stored flat within seconds.
There are a few different tutorials for building this chair on Instructables, and they all have the same concept. One board is slotted through the other which creates a base to sit on. No glue, screws or nails are required.
Start with a 2x8x12 piece of lumber. Use your circular saw to cut a 48" board for the back and to cut notches for the seat. You'll need a drill and jigsaw to cut a hole in the back for the slot board to fit through.
One Board Minimalist Chair [Instructables]