Heat olive oil in a large skillet over medium-high heat.
Add the sliced chicken breasts to the skillet and season with salt, black pepper, and dried oregano. Cook for 5-6 minutes, stirring occasionally, until the chicken is cooked through and slightly browned. Remove chicken from skillet and set aside.
In the same skillet, add the sliced green bell pepper, red bell pepper, and yellow onion. Sauté for 5-7 minutes until the vegetables are softened and slightly caramelized.
Add the minced garlic to the vegetables and cook for an additional 1 minute until fragrant.
Return the cooked chicken to the skillet with the vegetables and stir to combine.
Divide the chicken and vegetable mixture evenly into four sections in the skillet. Place one slice of provolone cheese on top of each section. Cover the skillet with a lid or aluminum foil and cook for 2-3 minutes until the cheese melts.
While the cheese melts, slice the hoagie rolls lengthwise without cutting all the way through. Spread softened butter on the cut sides of each roll.
Toast the hoagie rolls in a separate skillet or under a broiler until golden brown.
Scoop the cheesy chicken and vegetable mixture onto each toasted hoagie roll.
Serve immediately and enjoy your skillet chicken cheesesteak!