Season the chicken breasts with salt and pepper. In a small bowl, whisk together the balsamic vinegar and olive oil. Brush this mixture onto both sides of the chicken.
Grill the chicken for 6-7 minutes per side or until fully cooked through, with no pink in the center.
While the chicken is grilling, prepare the strawberry salsa. In a medium bowl, combine the diced strawberries, red onion, jalapeño (if using), chopped basil, lime juice, and honey or agave nectar. Mix gently to combine.
Once the chicken is done, remove it from the grill and let it rest for a few minutes before serving.
Top each grilled chicken breast with a generous scoop of the strawberry salsa.