If using a charcoal grill, grill the chicken over direct, medium-high to high heat for 4-6 minutes per side. If using a gas grill, grill the chicken over direct heat for 4-6 minutes per side with a grill temperature (lid closed) about 400°- 450°.
If you are grilling vegetable kebabs too, choose hearty vegetables that are good for grilling. Place the vegetables (or vegetable chunks) in a bowl and toss them with some olive oil, salt, pepper and oregano and then thread them through skewers. Depending on their size, the cooking time should be just about the same with the chicken kebabs. Grill until you see some nice grill marks, turning every three minutes or so and brushing them with the seasoned olive oil.