Just building on ideas posted here, you could cut up two egg cartons into strips, then put a flat paper sized piece of cardboard on both sides. Keep the center area hollow, then fill it loosely with cotton yarn or similar, ripped up cotton balls perhaps, but somewhat loose, with the chip in the center. Essentially make a box with cut egg-carton strips, to withstand being crushed to some extent, but leave the center hollow with airy cushioning for the chip.
Edit: and wrap the whole thing with a few layers of moving tape