Preheat the broiler. Line a baking sheet with foil. Toss the tomatoes, lettuce, red onion, cilantro and lime juice in a medium bowl; season with salt and pepper. Set aside.
Toss the chicken with the chili powder and a generous pinch each of salt and pepper. Heat the olive oil in a large skillet over high heat. Working in batches, add the chicken and cook, flipping, until well browned but not fully cooked through, about 2 minutes. Transfer to the prepared baking sheet and top evenly with the cheese. Broil until the cheese melts and the chicken is cooked through, about 1 minute.
Combine the yogurt and 1 tablespoon water in a small bowl. Stir in the lime zest and a pinch of salt.
Divide the salad among plates and top with the chicken and tortilla chips. Drizzle with the lime yogurt and sprinkle with cilantro and pepper.