Place butter and oil in a large skillet and preheat the skillet over medium-high heat until hot.
Liberally sprinkle chicken breasts with salt and pepper, then place into the pan. Do not cover the pan.
Reduce the heat to medium and cook until the meat is no longer pink and the juices run clear. This should take 8 to 12 minutes. As the chicken cooks, turn it occasionally so it browns evenly. If the poultry browns too quickly, reduce the heat to medium-low. The Chicken breasts are done when the meat is no longer pink and the juices run clear.
While still in the pan, crumble goat cheese over the tops of chicken breasts. Top with sun dried tomatoes and fresh basil. That's it. Easy peasy!
*Chiffonade of basil is a simple stack, roll, and slice. Stack the leaves on top of each other, gently roll them into a cigar, and then use a sharp knife to slice them into thin ribbons. Nothing more than that!