Heat olive oil in a large skillet over medium-high heat.
Add the thinly sliced chicken breasts to the skillet. Season with salt, black pepper, and smoked paprika. Cook for 5-6 minutes, stirring occasionally, until the chicken is cooked through and lightly browned.
Add the sliced bell peppers, onion, and minced garlic to the skillet with the chicken. Cook for an additional 5-6 minutes, stirring frequently, until the vegetables are softened.
Reduce heat to low. Evenly distribute the chicken and vegetable mixture in the skillet and place one slice of provolone cheese over each quarter of the mixture. Cover the skillet with a lid and cook for 1-2 minutes until the cheese is melted.
While the cheese melts, slice the hoagie rolls lengthwise without cutting all the way through. Spread a thin layer of butter on the cut sides of each roll.
Heat a separate skillet or griddle over medium heat and toast the hoagie rolls, buttered side down, for 1-2 minutes until golden and crisp.
Divide the chicken cheesesteak mixture into four portions and scoop each portion into a toasted hoagie roll.
Serve immediately and enjoy your skillet chicken cheesesteak!