Step 1To remove the backbone from the chicken, use a large, sharp knife or very sharp kitchen shears and work on a secure cutting board. The best way to do this is to place a dampened towel on top of your work surface and set the cutting board on top of it. Hold the chicken upright, so that its back faces you. The back will come out in a long strip about 1¼ inches wide, so place your knife a little more than ½-inch to the right of the spine and cut down the length of the back. I find it easiest if you go down one side halfway, then the other side halfway, and so on, until the entire back is cut out. It generally takes a few cuts to do this. Discard the backbone.
Step 2Lay the chicken flat, with the uncut side facing up. In some cases, the breastbone may need to be pushed on a bit to flatten it more. The legs should be pointing outward from the body rather than inward toward each other. Separate the breast meat from the skin and slip about half of the thyme leaves under the skin on the surface of the meat. Repeat for the thighs with the remaining thyme. Rub one-quarter of the salt over the underside of the bird and rest on the skin side, making sure to get some under the wings and thighs. There should be a little less on the wings and a little more on the breast, legs, and thighs. Place the bird skin-side up on a platter and refrigerate, uncovered, for at least 3 hours or up to 1 to 2 days.
Step 3When you are ready to roast the chicken, place a pizza stone on the floor of your oven and heat the oven to 450 degrees for at least 30 minutes. Transfer the chicken to a baking sheet and set it aside to come to room temperature while the oven and stone are preheating.
Step 4Set the baking sheet directly on the stone and roast the chicken for 25 to 35 minutes, rotating the baking sheet after about 15 minutes so the chicken cooks evenly. Use an instant-read thermometer to check for doneness. The center of the thigh should reach 170 degrees and the thickest part of the breast should reach 160 degrees (it will continue to cook after it comes out of the oven). Remove the pan from the oven.
Step 5Transfer the chicken to a cutting board and cool for at least 10 minutes before slicing and serving.