In a medium bowl, toss the chickpeas, cucumber, basil, and shallot with the oil, vinegar, and ¼ teaspoon each salt and pepper.
Heat grill to medium. In a small bowl, combine the sesame seeds, paprika, ½ teaspoon salt, and ¼ teaspoon pepper.
Remove the skin from the chicken and discard. Sprinkle the chicken with the sesame seed mixture, pressing gently to help it adhere. Grill, covered, until cooked through, 9 to 10 minutes per side. Serve with the chickpea salad.