Divide chopped lettuce among serving plates. Top with halved cherry tomatoes and cubed avocado. Set aside.
Heat olive oil in a sauté pan over high heat. Add sliced chicken, garlic, thyme, salt, and pepper. Sear for about 5 minutes, or until the chicken is cooked through and lightly browned.
Pour the fresh orange juice over the cooked chicken. Allow it to boil vigorously, then immediately remove the pan from the heat. Stir in the cold butter until melted and the sauce is slightly thickened.
Spoon the cooked chicken over the prepared salads. Top with chopped pecans.
Drizzle the warm orange butter sauce over each salad or serve it on the side. Serve immediately.