Preheat a grill to high. Preheat the oven to 400 degrees F.
In a medium-sized bowl, mix together the cumin, coriander, paprika, cayenne, salt, pepper, to taste, lemon juice, lemon zest, yogurt, garlic and ginger root until well incorporated. Add chicken and evenly cover with marinade. Cover with plastic wrap refrigerate for 1 to 2 hours.
Remove the chicken from the marinade and put on the grill. Cook for 6 to 7 minutes on each side, turning frequently. Baste with remaining marinade while cooking. Lower heat to low and cover with grill lid. Continue to cook until the chicken is cooked through, about 18 to 20 minutes. Put the grits on a serving platter. Remove the chicken from the grill and serve on top of the grits.
In a heavy-bottomed large saucepan over medium-high heat, add the butter. Add onion and garlic and cook until softened, about 1 to 2 minutes. Stir in the milk and cream and bring to a boil. Whisk in the grits, then lower the heat and simmer, stirring frequently, until thick and tender, about 35 to 40 minutes. Add the Parmesan, lemon juice, salt, pepper and chives. Stir well. Keep warm until ready to use.