In shallow pie pan or dish, mix together flour, salt and pepper. In second shallow dish or pan, beat eggs lightly. In third shallow dish or pan, place breadcrumbs.
One at a time, dip each chicken breast half first into the flour mixture, coating thoroughly and dusting off excess. Dip chicken breast next in egg, covering completely. Finally, coat chicken with bread crumbs. Place each breaded chicken breast half on plate or on small sheet pan.
In large, non-stick skillet, place vegetable oil and butter. Warm over medium heat. Place chicken in skillet, cooking while turning, browning very well on both sides, about two minutes per side. Transfer chicken to paper-towel-lined plate or sheet pan.