Preheat grill. Brush chicken with olive oil and season with salt and pepper to taste. Grill for 5 minutes on each side or until cooked through, remove and let rest. Toss potatoes in olive oil and season with salt and pepper to taste. Grill cut side down until golden brown, turn over and continue grilling until cooked through.

Place 8 tortillas on a flat surface. Divide both cheeses among the tortillas. Slice chicken on the bias into 1/4-inch thick slices. Cut each potato half in half. Divide the chicken, potatoes, garlic and thyme among the 8 tortillas. Stack tortillas to make four. Top the four tortillas with the remaining four tortillas. Brush the top with olive oil and season with salt and pepper to taste. Grill, oil side down until golden brown. Carefully flip over and continue grilling until golden brown and the cheese has melted.