BRING water to boil in medium saucepan. Add quinoa; cover. Simmer on medium-low heat 15 min. or until liquid is absorbed.
MEANWHILE, heat 1 tsp. oil in large skillet on medium-high heat. Add chicken; cook 5 to 7 min. on each side or until done (170ºF), adding 2 Tbsp. dressing to skillet for the last minute. Transfer chicken to plate; top with reserved pan drippings. Cover to keep warm.
ADD remaining oil, carrots, ginger and garlic to skillet; cook 3 to 5 min. or until ginger and garlic are fragrant, but not browned, stirring frequently. Stir in bok choy; cook 1 to 2 min. or until bok choy begins to wilt. Add remaining dressing; cook 2 min. or until carrots are crisp-tender and liquid comes to boil, stirring frequently.
SPOON quinoa onto serving plates; top with vegetable mixture and chicken.