In a small bowl, mix together the salt, pepper, thyme and lemon zest. Sprinkle the chicken on both sides with all but 1/2 teaspoon of the mixture. Place the chicken skin-side up in a large (5-quart) braiser or cast-iron skillet. Nestle the tomato halves and fennel wedges around the chicken; season the vegetables with the remaining salt mixture. Drizzle the chicken and vegetables with the olive oil.
Cover the pan and place in the oven for 20 minutes. Uncover and return to the oven for about another 20 minutes, until the chicken is golden brown and an instant-read thermometer inserted into the thickest part of the breast reads 160 degrees F. Let rest for 15 minutes before carving.
Serve the chicken alongside the vegetables, drizzled with pan juices and sprinkled with the basil.