Stir together the cream cheese, Cheddar cheese and jalapenos in a small bowl.
Cut a pocket horizontally through the thickest side of each chicken breast, and fill with 1/4 of the cheese mixture. Secure with toothpicks.
Roll the chicken breasts in bread crumbs to coat. Heat the oil in a frying pan over medium-high heat, and cook chicken breasts until no longer pink in the center and the juices run clear, about 8 minutes per side. An instant-read thermometer inserted into the center should read at least 74 degrees C.