Tear off two sheets of aluminum foil, each about 18 inches square, and place one on top of the other. Use the olive oil to smear a patch in the center of the foil, large enough to hold the chicken. Make a bed of the tomato slices, in the center, then top with the chicken breasts, salt and pepper to taste, the Parmesan, and thyme leaves. Add the olives and thyme sprigs.

Fold the foil over the chicken onto itself and crimp the edges as tightly as possible by making 1- or 2-inch folds, one after the other, each sealing the other. Seal the package very tightly, but leave plenty of room around the chicken. (You can prepare the recipe up to 3 hours in advance to this point; refrigerate the package.)

Place a skillet large enough to hold the package over high heat. A minute later, add the remaining oil, then pour out all but a film. Put the package in the skillet; it will sizzle. About 2 minutes later, the package will expand like a balloon; be careful of the escaping steam. Cook for 5 minutes longer from that point.

Remove the package from the heat, again taking care to avoid any escaping steam. Let rest for 1 minute, then cut a slit down the length of the top with a knife. Use a knife and fork to open up the package, then spoon the chicken, garnish, and juices onto a plate and serve.