Place chicken strips in 1-gallon reclosable plastic bag. Add lime juice, brown sugar, 1 T of the oil, and 1 t of the garlic. Seal bag and mix all ingredients together well. Marinate in refrigerator for 4 to 6 hours. Drain off and discard marinade. In large skillet, over medium-high heat, cook chicken until fully cooked and lightly browned; set aside. Prepare pizza dough according to package directions. Press dough evenly into greased 12-inch pizza pan. Brush dough with remaining 1 T olive oil, spread with remaining 1 t of minced garlic, and sprinkle with basil. Top with cooked chicken and cheese. Bake in 400 degree oven for 15 to 18 minutes.