Finely shred peel from orange & set aside. Juice orange. In medium saucepan, combine applesauce, vinegar, cardamom, juice from the orange and a 1/2 tsp. each salt & black pepper. Bring to boiling over high heat. Reduce heat to low. Cook, uncovered, stirring occasionally, 10 minutes. Remove from heat and cover to keep warm.
Season chicken lightly with salt & pepper. Heat oil in 12" nonstick skillet over medium high heat. Add chicken; cook until golden brown on bottom, about 4 minutes. Turn chicken and add 1/2 cup of the applesauce mixture to skillet. Cook 2 to 3 minutes more or until chicken is cooked through.
To serve, top chicken with some of the applesauce mixture, orange peel, and fresh thyme if desired.
Pass remaining applesauce mixture.