Preheat oven to 450 degrees. Thinly slice garlic. Halve and thinly slice fennel, leaving the core intact. Stem and seed bell peppers, and cut into 1/2-inch slices. Divide vegetables, grapes, and chickpeas, rinsed and drained, between two rimmed baking sheets.
Drizzle each sheet with oil and toss with oregano, salt, and pepper, to taste.
Place in oven and roast, rotating sheets once, until vegetables are golden brown and grapes are beginning to burst, about 25 to 30 minutes. Remove vegetables and any pan juices; transfer to a serving platter. Serve warm.