Place the chicken breast halves into a saucepan, and fill with enough water to cover. Bring to a boil, and cook until the chicken is cooked through, about 20 minutes. Remove from the water, and set aside to cool.
Preheat the oven to 375 degrees F (190 degrees C). Remove the chicken meat from the breasts, and discard the skin and bones. Set aside.
Heat the olive oil in a large skillet over medium heat. Add the green chilies, jalapeno and garlic. Cook and stir for a few minutes, until fragrant, then stir in the cream cheese and half of the Monterey Jack. As the cheese begins to melt, gradually stir in the water. Chop the chicken meat, and stir into the skillet. Remove from the heat.
Spoon the chicken mixture into tortillas, and roll up. Place the rolls seam side down in a 9×13 inch baking dish. Sprinkle the remaining Monterey Jack cheese over the top, then pour cream over all.
Bake for 30 minutes in the preheated oven, or until the enchiladas are golden brown on the top.
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