Preheat the grill to medium-high heat.
In a small bowl, mix olive oil, garlic powder, dried oregano, salt, and black pepper.
Brush the chicken breasts with the olive oil mixture on both sides.
Place the chicken breasts on the grill and cook for 6-7 minutes per side or until the internal temperature reaches 165°F (75°C).
Remove the chicken from the grill and let it rest for 5 minutes, then slice into strips.
In a medium bowl, whisk together mayonnaise, lemon juice, Dijon mustard, minced garlic, chopped anchovy fillets, Worcestershire sauce, and freshly ground black pepper until smooth to make the Caesar dressing.
In a large salad bowl, combine chopped romaine lettuce, croutons, and grated Parmesan cheese.
Pour the Caesar dressing over the salad and toss gently to coat evenly.
Divide the salad onto four plates and top each with sliced grilled chicken.
Serve immediately.