Preheat grill. Brush chicken breasts with 1 tablespoon of olive oil and season with salt and pepper to taste. Grill breasts on each side for 4 to 5 minutes, remove and let rest. Toss the potatoes in the remaining olive oil and season with salt and pepper to taste. Grill flesh side down for 2 to 3 minutes until golden brown, turn over and continue cooking until tender. Place 4 tortillas on an ungreased baking sheet. Spread each tortilla with 2 tablespoons of each cheese, 4 slices of chicken, 1 clove of garlic and 4 potato halves. Sprinkle each tortilla with fresh thyme. Stack the 2 layers and cover with the remaining 2 tortillas. Brush the top tortillas with vegetable oil place oilside down on the grill. Cook on one side until golden brown, turn over and continue cooking until the cheese melts. Cut into quarters and serve immediately.
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