If using wooden skewers, first soak the skewers in water for at least five minutes to prevent the wooden skewers from burning.
While soaking the wooden skewers, Place all of the season ingredients in a blender and blend until the mixture if finely ground.
Cut the chicken breast into cubes. Then, place the chicken pieces and tomatoes on each skewer.
Season the chicken skewers with salt, pepper, and four tablespoons of the Greek seasoning.
Heat the pesto in small saucepan using medium heat until pesto is heated through.
Grill chicken skewers for four to five minutes on each side or until chicken is cooked through and no longer pink.
Brush cooked chicken skewers with warmed pesto sauce.
Use remaining pesto sauce as a garnish and dipping sauce.