Heat 1 teaspoon of olive oil in a pan over medium heat. Season the chicken breasts with salt and pepper to taste and add them to the pan.
Cook for 4-5 minutes on each side, or until browned and cooked through. Cut the chicken into thick slices and set aside.
In a small bowl whisk together the remaining olive oil, balsamic vinegar, honey, Dijon mustard and salt and pepper to taste.
Pour the dressing over the greens and toss to coat. Arrange the chicken on top of the greens along with the goat cheese, pear, walnuts, and pomegranate arils. Serve immediately.