Combine chicken breasts and teriyaki marinade in a large resealable plastic bag. Marinate in the refrigerator for at least 1 hour.
Combine cilantro, peanut butter, red wine vinegar, lime juice, brown sugar, garlic, sesame oil, and lime zest in a food processor; blend well. Pour in 1/2 cup olive oil slowly and blend until dressing is smooth. Add pepper; blend again.
Preheat oven to 350 degrees F (175 degrees C). Spread corn tortilla strips on a baking sheet; drizzle 2 teaspoons olive oil on top.
Bake in the preheated oven until crispy, 5 to 10 minutes.
Heat 2 tablespoons olive oil in a skillet over medium heat. Add chicken breasts; cook until browned, 7 to 10 minutes per side. Cool until easily handled, about 5 minutes. Slice into thin strips.
Toss corn, black beans, and romaine lettuce together in a large bowl. Top with Monterey Jack cheese, chicken, and tortilla strips. Pour dressing over salad.