1. Light a grill or preheat a grill pan. Brush the chicken breasts with olive oil and season with salt and pepper. Lightly brush the grate or grill pan with vegetable oil and cook the chicken over a hot fire until browned and just cooked through, about 3 minutes per side. Transfer to a plate and let cool to room temperature.
2. In a medium saucepan of boiling water, blanch the chard leaves for 1 1/2 minutes; blanch the spinach for 30 seconds. Drain well. Let cool slightly, then squeeze dry and coarsely chop. In a large bowl, mix the chard with the 2 tablespoons of olive oil and season with salt. Stir in the drained yogurt and the garlic and season with salt and pepper.
3. For each wrap, arrange 2 sheets of lavash on a work surface, overlapping the short sides by 5 inches. Tuck half of the cheese slices under the overlapping flap to within 1/2 inch of the edge. Spread half of the avocado slices on top of the overlapping flap and sprinkle with half of the lemon juice; season generously with salt, pepper and hot sauce. Top with half of the tomato slices and season with salt and pepper. For each wrap, fold 1 of the flaps of lavash over the tomatoes and spread half of the chard on the lavash. Top with a chicken breast, trimming it to fit. Fold the second lavash flap over the chicken. Repeat to assemble the second sandwich. Tightly wrap the sandwiches in foil and refrigerate until firm or for up to 4 hours.
4. Light a grill. Unwrap the sandwiches and brush both sides with olive oil. Lightly brush the grate with vegetable oil. Grill the sandwiches over a low fire, cheese side down, for about 4 minutes, or until the cheese melts and the lavash is crisp. Using 2 large spatulas, carefully flip the sandwiches and grill for 5 minutes longer, or until they are heated through and very crisp. Transfer to a cutting board. Using a serrated knife, cut each sandwich crosswise into thirds and serve.
Wine Recommendation: An ice-cold, very dry pilsner-style beer, such as Pilsner Urquell or Grolsch, will pair well with the tangy, spicy flavors of this sandwich.