In a small bowl, soak dried apricots in apple cider until plump, 5 minutes.
With an immersion blender, puree apricots with cider, and canned apricots in juices, until smooth. Set aside.
In a large skillet heat oil. Brown chicken breast on both sides, about 3 minutes each side. Transfer chicken to plate.
Add shallots to pan and cook until lightly browned, 2 minutes.
Add broth, orange juice, rosemary, chili powder and sugar.
Return chicken to pan and simmer until cooked through, 6 to 8 minutes.
Add salt and pepper. Remove chicken from pan.
Add pureed apricot mixture and cook until sauce is slightly reduced and thickened, about 5 minutes.
Serve chicken with sauce.