Preheat the oven to 400 degrees.
Cut a long slit in the sides of the chicken, almost completely through to the other side.
Cut each slice of cheese into three long pieces and stack together.
Tuck the stacked cheese into each green chile.
Stuff the green chiles into the chicken breasts.
Close the slit with toothpicks.
In an oven proof skillet, heat the oil over medium high heat.
Place the chicken in the skillet and cook 3-4 minutes until golden brown on that side.
Flip the chicken over and place the skillet into the pre-heated oven.
Cook for 20 minutes, or until the chicken is cooked all the way through.
Let the meat rest on the counter for 5 minutes prior to slicing.
Slice thinly and serve while it is still warm and melting with cheese. Enjoy!