Preheat oven to 425 degrees. Spray nonstick baking pan with nonstick spray.
With fork, mix together feta, sun-dried tomatoes, basil, salt, and pepper in a small bowl. Spread Panko on sheet of wax paper.
With small, sharp knife, cit pocket, about 21/2 inches long in each chicken breast. Put one-fourth of cheese mixture into each pocket and press edges closed. Brush top of each breast with mayonnaise. Press coated side of chicken, one breast at a time, into thr bread crumbs. Place, coated side up in prepared baking pan.
Lightly spray each breast with nonstick spray. Bake chicken until completely cooked and crust is golden, about 25 minutes.