Heat an outdoor grill or indoor grill pan to high. Season the chicken with salt and pepper, and drizzle with EVOO to keep it from sticking to the grill. Cook for 3-4 minutes on each side and transfer to a foil-covered platter to hold. If you are using a grill pan, cook the chicken in 2 batches if necessary. While the chicken cooks, make the sauce.
Place a medium pot on the stove over medium heat. Add 2 tablespoons of the EVOO (twice around the pan). Add the garlic, red pepper flakes and onion. Cook for 10 minutes, stirring often. Add the tomatoes and heat through, 2 minutes. Wilt in the basil and season the sauce with salt and pepper.
Preheat the broiler to high.