Mix Greek yogurt, cilantro, lemon juice, garlic, salt, cumin, cayenne, and pepper together in a large bowl. Place chicken thighs in a large resealable plastic bag; cover with yogurt mixture.

Let chicken marinate in the refrigerator, 3 to 8 hours.

Bring chicken to room temperature, about 30 minutes. Pour off marinade.

Preheat grill for medium heat and lightly oil the grate. Grill chicken, turning occasionally, until grill marks form, about 5 minutes per side.