Place a chicken breast on a cutting board. Take a sharp knife and, holding it parallel to the chicken, make a 1-inch-wide incision at the top of the breast. Carefully cut into the chicken to form a large pocket, leaving a ½-inch border along the sides and bottom. Repeat with the other 3 breasts.
Place the cheese in a bowl and add the jalepinos. Stir well to combine. Place mixture into a large ziplock. Cut a ¾-inch hole in one corner of the plastic bag with the jalepeno cheese, then squirt the softened cheese into the pockets in the chicken, dividing the cheese evenly among them.
Wrap 2 strips of bacon around each breast and secure the ends with toothpicks. Place the bacon-wrapped Chicken onto a rimmed baking sheet and place in the oven. Cook until the bacon is crisp and the chicken is cooked through, about 18-20 minutes. Timing will depend on how thick the chicken breast is.
Store in an airtight container in the refrigerator for up to 3 days. To reheat, place on a rimmed baking sheet in a 400 degree F oven for 5 minutes or until warmed through.