Place the chicken breasts between sheets of plastic wrap and gently pound to an even thickness for uniform cooking.
Combine the vegetable oil, key lime juice, salt, paprika, dried basil, onion powder, crushed thyme, and garlic powder in a bowl and whisk until blended.
Put the chicken in a zip-top bag or shallow dish and pour the marinade over it, ensuring all pieces are coated; seal and refrigerate to marinate overnight.
Remove the chicken from the refrigerator 1 hour before cooking to come closer to room temperature.
Prepare your grill or heat a cast iron grill pan to medium-high heat and oil the grate or pan lightly to prevent sticking.
Grill the chicken breasts until cooked through and the internal temperature reaches 165ºF, flipping as needed for even charring; timing will vary but should take about 15 minutes total.
Remove the chicken from the grill and let it rest a few minutes before serving.