Flatten each chicken breast to 1/4-inch thickness. Place a slice of ham and cheese on top of each chicken breast.
In a shallow dish, mix together the flour, salt, and pepper. Dip each chicken breast into the flour mixture, coating both sides.
In a large skillet, heat the butter and olive oil over medium-high heat. Add the chicken breasts and cook until golden brown, about 3-4 minutes per side.
Add the wine and chicken broth to the skillet. Bring to a boil, then reduce heat to low and simmer for 10 minutes, or until the chicken is cooked through.
Serve with a sprinkle of minced fresh parsley, if desired.
Interesting Facts
Chicken cordon bleu originated in Switzerland in the 1950s.
The dish is named after the French cooking term "cordon bleu," which translates to "blue ribbon."
Chicken cordon bleu is often served with a creamy mustard sauce.