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HEAT grill to medium-high heat.
PLACE beets in medium microwaveable bowl; cover with waxed paper. Microwave on HIGH 6 min. or until crisp-tender. Remove from bowl; set aside. Add carrots to same bowl; cover with waxed paper. Microwave 3 min. or until crisp-tender.
MEANWHILE, mix dressing and honey until blended. Remove 1/4 cup dressing mixture; mix with mayo. Reserve for later use. Toss chicken with 3 Tbsp. of the remaining dressing mixture.
THREAD each chicken thigh onto 2 skewers. Thread beets, carrots and peppers alternately onto additional skewers.
GRILL chicken and vegetables 15 min. or until chicken is done (165ºF), turning and brushing all skewers with remaining dressing mixture for the last 5 min. and adding pitas to the grill for the last 3 min.
SERVE chicken and vegetables with pitas and the reserved mayo mixture.