In a large bowl, combine cubed chicken and basil pesto. Cover, refrigerate and let marinate for at least 1 hour and up to 1 day.
When ready to cook, thread chicken and tomatoes onto skewers, alternating each as you go.
Preheat outdoor grill or indoor grill pan over medium heat. Lightly grease grates with nonstick cooking spray. Once hot, place skewers on grill and cook for 3-4 minutes. Flip and continue cooking until chicken is cooked through, 2-3 more minutes.