To prepare vegetables, trim off beet roots; peel beets. Cut each beet into 6 wedges. Place beet wedges in an 11 x 7-inch baking dish. Cover and microwave at HIGH for 5 minutes; cool slightly. Add broccoli florets and carrot slices; sprinkle with water and 1/4 teaspoon salt. Cover and microwave at HIGH for 10 minutes or until tender. Remove the vegetables with a slotted spoon, and place in a shallow serving dish.
To prepare the aioli, place sour cream and the next 5 ingredients (sour cream through garlic cloves) in a blender or food processor; process until smooth, scraping sides of bowl once. Place garlic mixture in a small bowl; stir in chives. Serve with vegetables.