In a mixing bowl, combine the brown sugar, balsamic vinegar, water, Dijon mustard, and dried thyme. Whisk until the sugar is dissolved. Add the chicken breasts to the marinade, ensuring they are well coated. Allow the chicken to marinate for at least 30 minutes, or up to 2 hours for maximum flavor.
Heat the olive oil in a grill or skillet over medium-high heat. Remove the chicken from the marinade (discarding the excess marinade) and place it on the hot grill or skillet. Cook for about 6-7 minutes on each side, or until the chicken is cooked through and has nice grill marks. The internal temperature should reach 165°F. Once done, remove the chicken from the heat and let it rest for a few minutes before slicing.
In a large salad bowl, add the washed and dried baby spinach or mixed greens. Top with sliced strawberries, avocado slices, and thinly sliced red onion.
After the chicken has rested, slice it into strips. Arrange the sliced chicken on top of the salad.
Sprinkle the chopped pistachios over the salad for an added crunch. Drizzle with any remaining balsamic dressing if desired, or serve it on the side for guests to add to their liking.