Add vinegar, 1/4 teaspoon salt, 1/8 teaspoon pepper, mustard, and maple syrup to a large bowl. Smash garlic with the back of a knife and add to the bowl as well. Stir to combine, and allow to rest while you prepare the other ingredients.
Drain and rinse chickpeas, slice celery into 1/4 inch pieces (Save the leaves for later! You’ll need about 2 cups), and slice green onions. Slowly add oil to the garlic mixture, whisking constantly. This mixture will come together and emulsify. Add chickpeas, celery, and onions. Toss to coat evenly; cover and refrigerate for 2 hours (or up to, overnight).
Preheat grill (outdoors or indoors). Season chicken with remaining 1/4 teaspoon salt and pepper, paprika, and chili powder. Grill each side for approximately 4 minutes or until the inside is no longer pink; cover and set aside.
Chop celery leaves, halve tomatoes, and roughly chop basil. Remove the smashed garlic from the chickpea mixture, then add remaining chopped veggies. Toss again to combine, then top with Parmesan.
Place a large lettuce leaf onto each plate, then heap veggie mixture on top. Cut up chicken and add to salad as well, or simply serve alongside.