Combine all of the ingredients for the marinade. Add the chicken and turn to coat. Let sit for 30 minutes.
Make the salsa. Heat 1 tablespoon oil in a saute pan over medium-high heat. Add the corn and cook until charred. Let cool. Toss the corn with tomatoes, jalapeno, red onion, cilantro, and lime juice. Season with salt and pepper. Let sit for 20 minutes to let the flavors develop.
Blister peppers on the stovetop over medium heat. Place pepper directly on the heat and cook until the skin has blackened, rotating to blacken the entire pepper. Remove and repeat with the remaining peppers. Place peppers in a medium bowl and cover with plastic. Let sit for 10 minutes. Remove cover and carefully peel the blistered skin, removing the blackened skin. Slice into strips, discarding the seeds.
Heat grill on medium-high. Add the chicken and cook until the juices run clear. Remove from the grill and let rest for 10 minutes. Slice the chicken.
Assemble salads. Place a bed of romaine onto the plates followed by the roasted peppers, avocado, chicken, and corn salsa. Sprinkle cotija on top and a squeeze of lime. Serve immediately.