In a medium saucepan heat oil over medium heat. Add shallot; cook for 3 minutes, stirring occasionally. Add broth, squash, and barley. Bring to boiling; reduce heat. Simmer, covered, for 10 to 12 minutes or just until squash and barley are tender, stirring once or twice. Stir in apple. Cook, covered, for 3 to 4 minutes more or just until apple is tender. Remove from heat; set aside.
Meanwhile, in a small bowl combine coriander, cumin, salt, turmeric, and cayenne pepper. Sprinkle evenly over all sides of the chicken breast halves. Lightly coat all sides of chicken breast halves with cooking spray.
Coat a grill pan or large nonstick skillet with cooking spray; heat over medium heat. Add chicken to hot pan or skillet. Cook for 8 to 12 minutes or until chicken is no longer pink (170 degrees F), turning once halfway through cooking. Remove chicken from pan. Slice chicken.
Add pumpkin seeds to barley mixture; stir until combined. In a small bowl stir together chutney and yogurt. Serve barley mixture topped with sliced chicken and the chutney mixture. Sprinkle with parsley.