Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Combine the rub ingredients. Season the cut sides of the limes, tomatoes, and zucchini slices with the rub. Brush the chicken on both sides with the oil and season evenly with the remaining rub.
Grill the chicken, bone side down, over indirect medium heat, with lid closed, until the meat is opaque all the way to the bone, 30 to 40 minutes. If desired, to crisp the skin, grill the chicken over direct heat during the last 5 to 10 minutes of grilling time, turning once. Remove from the grill and let rest for 3 to 5 minutes.
While the chicken rests, grill the limes, tomatoes, and zucchini over direct heat, with the lid closed, until the limes and tomatoes are warm and the zucchini are crisp-tender, 3 to 5 minutes, turning once.
Squeeze the grilled limes over the chicken and serve with the tomatoes and zucchini.