Heat 2 tablespoons of the oil in a large ovenproof skillet over medium-high heat. Season the chicken with the turmeric, coriander, ½ teaspoon salt, and ¼ teaspoon pepper. Cook, skin-side down, until the skin is golden brown and crisp, 6 to 8 minutes.
Turn the chicken skin-side up and transfer the pan to oven. Cook until an instant-read thermometer inserted in the center of the thickest breast (avoiding the bone) registers 165° F, 22 to 25 minutes.
Meanwhile, combine the chickpeas, avocado, shallot, cucumber, mint, vinegar, the remaining 2 tablespoons of oil, ½ teaspoon salt, and ¼ teaspoon pepper in a medium bowl.