Preheat the grill or grill pan to medium-high heat.
Brush the chicken breasts with olive oil and season both sides with salt and black pepper.
Grill the chicken breasts for 6-7 minutes on each side or until the internal temperature reaches 165°F (75°C) and the chicken is cooked through.
Remove the chicken from the grill and let it rest for 5 minutes.
While the chicken rests, place the chopped romaine lettuce in a large salad bowl.
Add the Caesar dressing to the lettuce and toss gently until the leaves are evenly coated.
Slice the grilled chicken breasts into thin strips.
Divide the dressed romaine lettuce evenly among four plates.
Top each plate with sliced grilled chicken, croutons, and sprinkle with freshly grated Parmesan cheese.
Serve immediately with lemon wedges on the side for squeezing over the salad.