Make the marinade/dressing:
In a small bowl, whisk all of the ingredients together, or shake together in a sealed mason jar; you should have about ⅓ cup. Transfer 2 tablespoons to a medium bowl, add the chicken breasts, toss to coat, and marinate for as long as you choose; even 15 minutes helps! To the remaining 4 tablespoons marinade/dressing, whisk in ¼ cup mayonnaise until smooth; this is your dressing!
Grill the chicken:
Heat a grill or grill pan over medium-high heat. Brush the grill pan lightly with oil, remove the chicken from the marinade, shake off any excess, and grill the chicken until it’s just cooked through, 3–4 minutes per side for small breasts or 5-6 for large. Remove to a cutting board and let rest for 5 minutes before slicing across the grain to the thickness you like!
Build the bowls:
Divide the lettuce, chicken, chickpeas, carrots, radishes, and scallions into bowls. Drizzle each generously with dressing and sprinkle with sesame seeds.