In small bowl, soak apricots in apple juice until tender, about 30 minutes. Drain; reserve 1/2 cup juice.

Sprinkle chicken with salt and paprika. In large skillet, heat oil over medium-high heat. Add shallots; saute 2 minutes. Add chicken and cook until lightly browned, 2 to 3 minutes per side. Add reserved 1/2 cup apple juice, wine, and nutmeg. Reduce heat to low; simmer covered 10 minutes. Stir in apricots; simmer covered 5 minutes more. Sprinkle with walnuts.