1. Combine first 3 ingredients in a small bowl. Sprinkle chicken with pepper mixture. Place a large grill pan over medium-high heat; coat pan with cooking spray. Add chicken to pan; cook 5 minutes on each side or until done. Cool slightly; shred meat.
2. Recoat pan with cooking spray. Place apricots, cut sides down, on pan; cook 6 minutes on medium-high heat or until tender and lightly browned, turning after 4 minutes. Place apricots and next 4 ingredients (through garlic) in a food processor; process until smooth.
3. Spread about 1/2 teaspoon apricot chutney over cut side of each sandwich bun half. Place about 1/3 cup chicken on bottom bun; cover with top half of bun.