In a small bowl, combine all the spices and brown sugar. Stir in the olive oil and mix until a crumbly, moist paste forms.
Place the chicken in a single layer in a 9X13-inch or similar size baking pan. Rub the chicken generously with the spice mixture on all sides. Cover the baking dish with plastic wrap and refrigerate for at least 2 hours or up to 10 hours.
Grill the chicken over medium heat until cooked through, about 6-7 minutes per side, depending on the size and thickness of the chicken breasts. Let the chicken rest for 5 minutes. Cut into strips and serve. This chicken is delicious served as-is and is also wonderful served in soft tortillas with taco garnishes.
Serving: this chicken is served delicious grilled with sides of your choice and is also delicious cut into strips and served in soft tortillas with taco/fajita garnishes.