Mix the sour cream, garlic, lemon juice, paprika, turmeric, brown sugar, curry, and Cayenne in a large bowl.
Spoon 3/4 cup of the mixture into a small covered container. Stir the tomato paste into the mixture in the small covered container and refrigerate.
Cut the chicken crosswise into 12 strips. Add to the remaining sauce mixture in a large bowl and stir to coat chicken completely. Cover and refrigerate for 1 hour to marinate.
Generously spray a grill rack with grill nonstick spray. Heat a gas or charcoal grill to medium heat. Grill the chicken for 3 to 4 minutes on one side. Turn and grill for an additional 3 to 4 minutes or until thoroughly cooked. Remove from the grill and insert wooden skewers through the strips to serve.