Preheat a grill or grill pan to medium-high heat.
Season the chicken breasts with salt and pepper if desired, then place them on the hot grill.
Grill the chicken until cooked through and no longer pink in the center, about 5–6 minutes per side depending on thickness.
In the final few minutes of cooking, top each breast with 1/2 ounce sliced provolone so it can melt.
During the last few minutes, place the buns cut-side down on the grill and toast until lightly browned.
Spread about 2 tablespoons Caesar dressing on each bun half.
Assemble the burgers by layering romaine leaves and sliced red onion (if using) on the bottom bun, then top with the grilled chicken and close with the top bun.
Serve immediately and enjoy.