To prepare chicken, combine first 5 ingredients in a large zip-top plastic bag. Seal and marinate in refrigerator 2 hours, turning bag occasionally.
To prepare vinaigrette, combine cilantro and next 8 ingredients (through dash of salt) in a small bowl; stir with a whisk. Chill until ready to use.
Preheat oven to 350°.
To prepare tortilla strips, place strips in a large bowl. Coat with cooking spray; toss. Combine cumin, 1/4 teaspoon salt, paprika, and dash of red pepper. Sprinkle over strips; toss well. Spread strips in a single layer on a baking sheet. Bake at 350° for 8 minutes or until almost crisp. Remove from oven; cool. (Tortilla strips will crisp as they cool.)
Remove chicken from bag, discarding marinade. Sprinkle chicken with 1/2 teaspoon salt. Place chicken on grill rack coated with cooking spray, and grill for 5 minutes on each side or until done. Cut chicken into 1/2-inch slices. Combine jicama, mango, and greens in a large bowl. Pour vinaigrette over jicama mixture, and toss to coat. Place 1 1/3 cups jicama mixture on each of 6 plates, and top each serving with 1 sliced chicken breast half. Top evenly with tortilla strips.