In a large bowl, whisk the first six ingredients. Pour 3/4 cup marinade into a large resealable plastic bag; add the chicken. Seal bag and turn to coat; refrigerate overnight. Cover and refrigerate remaining marinade.
Drain and discard marinade. Grill chicken, covered, over medium heat for 5-8 minutes on each side or until juices run clear. Cut into strips.
In a large bowl, combine the lettuces, blueberries, strawberries, cheese and walnuts. Add reserved marinade; toss to coat. Top with sliced chicken.