Whisk the garlic, honey, balsamic vinegar, basil and olive oil together in a bowl.
Put the chicken breasts in a large zip-top bag or shallow glass dish.
Pour the mixture over the chicken and turn each piece until well coated. Seal the bag or cover the dish and refrigerate for 4 hours.
Preheat a grill or grill pan to medium heat.
Remove the chicken from the marinade and discard the remaining marinade. Grill the chicken for about 5 minutes per side, depending on thickness.
The chicken is ready when the thickest part reaches 165°F (74°C). Rest it for 5 minutes before serving.