Pluck the thyme leaves from the stalks and roughly chop them. Mix the thyme with lemon zest, lemon juice, and olive oil. Place the chicken pieces and marinade in a freezer bag, seal it, and refrigerate for at least 30 minutes.
Soak 6 wooden skewers in lukewarm water during the marinating time. When the chicken has finished marinating, remove it from the freezer bag and reserve the marinade for basting.
Thread the chicken pieces onto the soaked skewers. Oil the grill grate thoroughly. Heat the grill to medium-high. Grill for 6-8 minutes total, turning to cook all sides evenly. After 3-4 minutes, brush the reserved marinade on both sides. Season with salt and pepper. Chicken is cooked when the internal temperature reaches 74°C (165°F).
Thread the chicken pieces onto the soaked skewers. Heat a coated pan to medium-high and add 2-3 tablespoons of olive oil. Pan-fry for 6-8 minutes total, turning to cook all sides evenly. After 3-4 minutes, brush the reserved marinade on both sides. Season with salt and pepper. Chicken is cooked when the internal temperature reaches 74°C (165°F).