In a large mixing bowl, whisk together the pesto, 2 tablespoons olive oil, garlic powder, lemon juice, 1 teaspoon salt and ½ teaspoon black pepper.
Add the chicken to the bowl and stir to make sure that the chicken is fully coated in the marinade. Cover and refrigerate for at least 1 hour but can be overnight as well.
Soak the wooden skewers in water for at least 15 minutes prior to using.
Toss the cherry tomatoes with the remaining olive oil, salt and black pepper.
Preheat a grill over medium high heat. Clean the grates and spray or rub oil onto the grates so that the kabobs do not stick while cooking.
Beginning and ending with a piece of chicken, thread the chicken and tomatoes onto the skewers evenly.
Place the chicken on the hot grill and cook for about 5-6 minutes per side until the chicken is cooked through (internal temperature of 165 degrees F). Cooking time total should be about 10-12 minutes and make sure to flip the kabobs every few minutes so that all sides are cooked evenly.
Remove the kabobs from the grill, cover loosely with foil and let them rest for about 5 minutes.
Then the kabobs are ready to serve and enjoy!