In a mixing bowl, whisk together the Greek yogurt, olive oil, lemon juice, lemon zest, minced garlic, minced ginger, cumin, coriander, paprika, cayenne, cinnamon, salt, pepper, and chopped cilantro until smooth and well combined.
Place the chicken pieces into a gallon-size resealable plastic bag.
Pour the yogurt marinade over the chicken, seal the bag while pressing out excess air, then massage the marinade so it coats the chicken evenly.
Refrigerate the bagged chicken for at least 2 hours; marinate up to 8 hours for breasts or up to 24 hours for thighs for best flavor.
Preheat a gas grill to 425°F (medium-high). Clean the grates and lightly oil them by wrapping a paper towel in tongs, dipping it in oil, and wiping the grates.
Grill the chicken until cooked through, about 5–7 minutes per side, or until an instant-read thermometer inserted into the thickest part reads 165°F.
If desired, brush the exterior lightly with olive oil halfway through grilling to help prevent drying.