Season chicken breasts with olive oil, salt, and pepper. Grill for 5-7 minutes per side, or until internal temperature reaches 165°F. Let rest 5 minutes, then slice into strips.
In a small bowl, whisk together mayonnaise, lemon juice, Dijon mustard, anchovies, garlic, and 1/4 cup Parmesan. Add water gradually until desired consistency. Season with salt and pepper.
In a large bowl, combine chopped romaine, remaining 1/2 cup Parmesan, and croutons. Add dressing and toss to coat.
Top salad with sliced grilled chicken. Serve immediately.
Tips
For extra flavor, marinate chicken in lemon juice, olive oil, and garlic for 30 minutes before grilling.
To make croutons, toss cubed bread with olive oil and garlic powder, then bake at 375°F for 10 minutes.
Leftover salad (without dressing) can be stored in the fridge for up to 1 day.