In a small bowl, whisk olive oil, vinegar, mustard, agave, garlic, pepper, and salt until smooth. Divide mixture in half and pour one half into a plastic bag. Arrange chicken breasts in plastic bag, seal and refrigerate chicken at least 2 hours.

Remove chicken from marinade and discard marinade (keeping reserved half cold in fridge) Grill chicken over medium-high heat, turning once until chicken registers 165F, about 15 minutes. Once chicken is cool enough to handle, slice into strips. Set aside.

Make the salad: In a large bowl, combine strawberries, mozzarella, avocado, lettuce, and grilled chicken strips. Drizzle reserved balsamic dressing over top and toss to coat. Sprinkle fresh basil on top of salad. Serve immediately.