Heat grill. In small bowl, mix oil and garlic. Brush chicken with 1 t of oil mixture. Sprink with salt. Place on grill over medium high heat. Cover grill and cook 12-18 min, turning once until juice is clear. The center should be 170 F. Reduce heat to medium low.
On ungreased cookie sheets, place tortillas. Brush with remaining oil mixture. Cut chicken into strips. Arrange chicken strips over tortillas. Sprinkle each with 1/4 c of cheese. Top evenly with tomato slices. Sprinkle with remaining cheese and basil.
With wide spatula, carefully slide the pizzas onto grill over medium low heat. Cover grill. Cook 3-5 min. rotate to avoid hot spots until cheese is melted and crusts are crisp. Slide pizzas back onto cookie sheets.
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