Cook quinoa according to package directions and fluff with a fork. Transfer to a large bowl and let cool.
Preheat broiler with a rack set 4 to 6 in. from heat. In a large bowl, stir together chili powder, 2 tsp. garlic, the lime zest, 2 tsp. oil, and 1/2 tsp. each salt and pepper. Add chicken and toss to coat. Put chicken on a baking sheet and broil, turning once, until browned and cooked through, about 12 minutes total. Let cool slightly, then slice and add to reserved quinoa.
Add remaining ingredients to quinoa and chicken; toss to coat.
Note: Nutritional analysis is per serving.