Preheat the grill to medium-high heat.
Brush the chicken breasts with 1 teaspoon olive oil and season both sides with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
Grill the chicken breasts for 5-6 minutes on each side or until the internal temperature reaches 165°F (74°C). Remove from the grill and let rest for 5 minutes.
While the chicken is resting, prepare the balsamic glaze by combining 2 tablespoons balsamic vinegar and 1 tablespoon honey in a small saucepan over medium heat. Bring to a simmer and cook for 3-4 minutes until slightly thickened. Remove from heat and let cool.
Slice the grilled chicken breasts into thin strips.
On a large serving platter, arrange the mixed salad greens as the base.
Layer the sliced tomatoes and mozzarella cheese evenly over the greens.
Place the grilled chicken strips on top of the tomato and mozzarella layers.
Scatter fresh basil leaves over the salad.
Drizzle the salad with 1 tablespoon extra virgin olive oil and the prepared balsamic glaze.
Serve immediately.