Halve the chicken breast into two equal sized thin pieces.
Season both sides of each chicken piece with salt and pepper.
Heat an oven-safe stainless steel skillet over medium heat. Add olive oil. Add chicken and fry for a few minutes on each side until starting to brown.
Place the skillet in the oven for 20-25 minutes or until cooked through and juices run clear. If you do not have an oven-safe skillet transfer the chicken to a baking dish and place the dish in the oven.
Meanwhile, mix together the jalapeño pepper, cream cheese, green onions, and cheddar cheese.
Remove the skillet from the oven and spread the cream cheese jalapeño mixture over the chicken. Return to oven and cook 5-10 minutes or until cheese is creamy and melted.