Cut the chicken breasts into thin strips and season with salt and black pepper. Heat butter and oil in a pan over medium heat. Add chicken strips and saute until lightly golden brown and cooked through, about 10-15 minutes.
Place them on a paper towel to absorb extra oil. Lay the sliced bread on a baking sheet. (Optional: spread a little mayonnaise on top of each slice of bread).
Arrange a single layer of cooked chicken strips on top of the bread.
Then top with tomato and chopped basil (as much as you like).
Top with Mozzarellas cheese.
Place under the broiler and broil until cheese is melted. Serve the open-faced chicken sandwich immediately.