In a medium bowl, mix together the paprika, garlic powder, salt, onion powder, thyme, cayenne pepper, and ground black pepper. Set aside about 3 tablespoons of this seasoning mixture for the chicken; store the remainder in an airtight container for later use (for seasoning fish, meats, or vegetables).
Preheat grill for medium-high heat. Rub some of the reserved 3 tablespoons of seasoning onto both sides of the chicken breasts.
Lightly oil the grill grate. Place chicken on the grill, and cook for 6 to 8 minutes on each side, until juices run clear.