Preheat the oven to 400 degrees F (200 degrees C).

Place carrots, potatoes, beets, onion, garlic, and chickpeas into a 9x13-inch baking dish; drizzle with olive oil, then season with thyme, salt, and pepper. Mix well.

Bake, uncovered, in the preheated oven for 30 minutes, stirring once midway through baking. Remove the baking dish from the oven, and stir in wine. Return to the oven, and bake until wine has mostly evaporated and vegetables are tender, about 15 minutes more. Stir in beet greens, allowing them to wilt from the heat of the vegetables. Season to taste with salt and pepper before serving.