Preheat a grill or grill pan on medium heat.
In a bowl lather the chicken with yogurt, lemon zest, salt and pepper. Set aside.
Combine chickpeas, onions, parsley, and garlic in a blender or food processor and blend until smooth.
Mix egg, cumin, lemon juice, baking powder, salt and pepper together in a bowl. Add chickpea mixture and mix together. Add bread crumbs slowly and combine using your hands until mixture isn't sticky, but will hold together when frying.
For the tahini sauce: Place the garlic in the lemon juice for 10 minutes. Remove the garlic, whisk in the tahini, salt, and pinch of cumin until thoroughly blended. (If you would like a thinner sauce whisk in some cold water by the tablespoon until it reaches your desired consistency)
Grill the chicken on both sides to an internal temperature of 160 degrees using a thermometer. Once cooked set aside to rest.
In the meantime, heat the oil for the falafel over medium heat in a nonstick pan. Form mixture into equal patties about as wide as the palm of your hand. Fry patties in the hot oil until browned, 3 to 4 minutes per side.
Drizzle the oil on the pita bread and season with salt and pepper. Grill the pita for 1 - 2 minutes per side to warm. Then cut into quarters.
Slice the chicken, serve with pita bread and falafel. Drizzle the sauce over top.