In small bowl stir together orange, lime, and lemon juices, 1 tablespoon oil, basil, 1/2 teaspoon of the salt, and 1/4 teaspoon pepper. Place chicken in resealable plastic bag set in large bowl. Pour juice mixture over chicken; seal bag. Refrigerate 1 to 4 hours, turning bag occasionally.
For dressing, in blender combine 1 cup of the blackberries, vinegar, sugar, mustard, oregano, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Cover and blend until smooth. With blender running, slowly add 1/2 cup oil in a thin steady stream until well combined. Transfer to serving container. Cover and refrigerate until serving time.
Drain chicken, discarding marinade. For charcoal grill, place chicken on the rack of an uncovered grill directly over medium coals. Grill for 12 to 15 minutes or until done (170 degrees F.), turning once. (For gas grill, preheat grill. Reduce heat to medium. Add chicken to grill rack. Cover and grill as above.)
Slice chicken. Divide greens among 4 serving plates. Top with chicken, pears, and remaining 2 cups berries. Top each with some of the dressing and feta cheese. Pass remaining dressing. Makes 4 servings.