Combine the shallots and vinegar in a bowl, cover, and refrigerate for at least a day and up to three days. (If you don't have time to do this step, just add the shallots to the roasting pan when you add the vinegar.)
Combine the thyme and olive oil in a blender and process until the thyme is completely incorporated into the oil. Cover and store the oil in the refrigerator up to 2 days; strain before using.
To roast the chicken, remove any giblets and pull off all excess fat. Rub the skin and the cavity with kosher salt, let the chicken sit for about an hour, and then wipe off all the excess salt. (This salting process is optional, but it gives the chicken a better flavor and texture.)
Heat the oven to 500°F. Brush the chicken generously with the thyme oil and season with freshly ground black pepper. Put the celery and onion in a flameproof roasting pan, season with salt and pepper, and then put the chicken on top of the vegetables. Roast the chicken at 500° for 15 minutes, then reduce the heat to 350° and continue cooking until the juices from the cavity run clear when the chicken is lifted, another 45 to 50 minutes. If the breast meat is cooking too quickly, cover it with a piece of buttered foil.
When the chicken is cooked, remove it from the roasting pan and keep it in a warm place. Put the roasting pan directly on a burner over medium-high heat. (Don't forget that the pan has been in the oven and will be very hot.) Add the vinegar to the veg etables and chicken juices in the pan (add the shallots, too, if you haven't infused them with the vinegar) and boil until the liquid is reduced by about half, scraping to dissolve any drippings.
Strain the liquid into a bowl and press on the vegetables with a spoon to extract their juices. Now whisk in the honey. Taste. The oil from basting and the accumulated chicken juices serve as the "oil" part of the vinaigrette, but if the sauce is too sharp, whisk in a little more thyme oil to mellow it. Season to taste with salt and pepper. Carve the chicken and pass the sauce at the table.