To make sauce, place balsamic vinegar, honey and soy sauce in a small bowl; mix well. Set aside.
Place water in 2-1/2 or 3-quart pot. Cover and bring to a boil over high heat. Add prepared carrots and rice; stir. Reduce heat to low and cook, covered, for 20 minutes or until all liquid is absorbed by rice. Remove from heat.
While rice and carrots are cooking, prepare chicken. Cut chicken into 3/4-inch chunks. Heat canola oil in 12-inch skillet over medium-high heat. Add chicken and 2 tablespoons sauce. Cook, stirring frequently, until chicken is cooked through. Add chopped green onions and sauté for an additional 30 seconds. Remove from heat.
Place cooked rice and carrot mixture in serving bowl. Add cooked chicken and green onion mixture, drained pineapple chunks, and remaining sauce; mix well. Serve hot.