Add the garlic, olive oil, balsamic vinegar, salt and black pepper to a food processor or blender.
Add most of the tomatoes and basil, reserving a little of each for serving.
Blend until combined.
Add the chicken and marinade to a large zip-top bag, making sure each chicken breast is well coated.
Seal the bag and refrigerate for 6 to 8 hours.
Preheat the grill to medium-high.
Grill the chicken for about 5 minutes per side, or until the thickest part reaches 165°F (74°C).
Remove the chicken from the grill and garnish it with the reserved tomatoes and basil.