Combine the mayonnaise, chili powder, cayenne and 1/2 teaspoon salt in a large bowl. Add the chicken and toss to coat. Cover and refrigerate at least 2 hours or overnight. Preheat a grill to medium low. Brush the grill grates with vegetable oil. Place the breadcrumbs in a shallow dish, then add the chicken, turning to thoroughly coat. Grill the chicken, turning once, until golden brown and cooked through, 20 to 25 minutes per side. Meanwhile, brush the tomatoes with vegetable oil and season with salt and black pepper. Place cut-side down on the grill and cook until marked, about 4 minutes per side. Serve with the chicken.