- Combine chickpeas, garlic, lemon juice, and tahini in bowl of a food processor. Process until thoroughly combined.
- With motor running, slowly add enough olive oil until a nice, smooth hummus is achieved. Season with salt.
- Heat grill to high. Place peppers and onion on grill and cook until skins are blackened. Remove from grill and let cool. Peel and discard skins and then slice into strips.
- Combine peppers, onion, chicken, oil, cumin, pepper, oregano, and basil in a baking dish and rest for one hour.
- Heat broiler with oven rack set 4—6 inches from heat. Broil, stirring once, until chicken is cooked through, about 8 minutes. Serve over hummus.