Pound chicken to 1/4″ thickness between 2 sheets of plastic wrap.
Combine flour, salt, pepper, and basil in a bowl and mix well.
Heat oil and butter in a sauté pan using medium heat.
Dredge chicken in seasoned flour mixture.
Cook chicken until lightly browned on the first side, about 4 minutes.
Turn chicken and cook about 2 minutes longer.
Remove chicken and add mushrooms. Cook about 6 minutes until lightly browned.
Add Marsala wine and simmer for 5 minutes.
Add chicken, reduce heat to medium-low; cover and simmer 10 minutes.