Preheat a grill or grill pan to medium-high and clean the grates.
Brush the chicken breasts with 1 tablespoon olive oil.
In a small bowl, mix 1/2 teaspoon ancho chili powder, 1/2 teaspoon ground cumin, 1/2 teaspoon kosher salt, and 1/2 teaspoon ground black pepper; sprinkle evenly over the chicken.
Grill the chicken until cooked through (internal temperature 165°F/74°C), about 6–9 minutes per side depending on thickness; remove and let rest on a plate until cool enough to slice.
While the chicken rests, arrange the torn romaine on a large platter or in a bowl and top with black beans, halved cherry tomatoes, sliced red bell pepper, corn kernels, and shredded cheddar.
Slice the rested chicken into strips and place over the salad.
Make the cumin-lime vinaigrette: whisk together 1/4 cup olive oil, 3 tablespoons cider vinegar, 2 teaspoons lime zest, 1 tablespoon lime juice, 1/2 teaspoon honey, 2 teaspoons chopped cilantro, 1 teaspoon ground cumin, 1 teaspoon Dijon mustard, 1/2 teaspoon garlic powder, 1/8 teaspoon cayenne, 1/2 teaspoon kosher salt, and 1/4 teaspoon ground black pepper until emulsified.
Drizzle the vinaigrette over the assembled salad and toss gently or serve vinaigrette on the side.
Serve with optional accompaniments such as guacamole, tortilla chips, warm tortillas, pickled red onions, or lime wedges as desired.