Heat the olive oil in a large skillet over medium heat.
Season the chicken breasts with salt and pepper. Add to the pan and cook for 5 to 6 minutes on each side.
While the chicken is cooking, whisk together the brown sugar, vinegar and water. Pour the mixture over the chicken and bring to a boil.
Continue cooking the chicken in the balsamic syrup for an additional 3 to 4 minutes until cooked through and no longer pink. Transfer to a platter and keep warm.
Remove the pan from the heat. Whisk in the mustard and thyme. Set aside.
Arrange the greens on a large platter. Top with the strawberries, avocado and red onion. Slice the chicken and arrange on top of the salad.
Sprinkle with pistachios and drizzle with the dressing. Serve immediately.