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.