1. Cook barley according to package directions. Let cool completely.
2. Meanwhile, preheat the oven to 400 degrees . Place chicken in a large straight-sided skillet or pot and cover with water by 1/2 inch. Bring to a boil over high heat; cover, reduce heat to medium low and cook 5 minutes. Remove from heat and let stand, covered, until the internal temperature reaches 160 degrees , 12 to 14 minutes. Remove chicken from water, let cool and shred.
3. Lightly coat a rimmed baking sheet with cooking spray and arrange eggplant in an even layer. Lightly coat eggplant with cooking spray and roast until golden brown, about 12 minutes. Remove from baking sheet and let cool.
4. In a large bowl, toss together chicken, eggplant, barley, tomatoes, mint, feta, onion, oil, lemon zest, lemon juice, salt and pepper.