In a medium sized saucepan, cover the chicken breasts with cool water. Put the chicken on the stove over medium heat and bring the pot to a boil. Turn off the heat, put a lid on the pot and set a timer for 20 minutes. After 20 minutes, take the chicken out of the pot and set it on a plate to cool for about 5 minutes before you shred it.
Turn on your oven to 350 degrees and spray a 9-inch square pan with cooking spray.
While the chicken is cooling, use an electric mixer to beat the cream cheese with the sour cream until it is smooth.
Add in half of the salsa and beat it again. Stir the shredded chicken into the mixture.
Scoop spoonfuls of this mixture into the tortillas, roll the tortilla around the chicken, and place it, seam side down in the prepared pan. Repeat with all the tortillas, leaving about ¼ cup of the mixture in the bowl.
Space the tortillas in the pan so that they cover the bottom of the pan.
Spread the remainder of the chicken mixture over the top of the tortillas in an even layer and top that with the rest of the salsa. Smooth these with a spoon, so they are evenly distributed over the top of the tortillas.
Sprinkle the cheese over the top of the tortillas.
Bake the pan uncovered in the center of your preheated oven for about 30 minutes. The cheese on top of the dish should be lightly browned and melted and the filling of the tortillas should be bubbling.
Take the pan from the oven and use a spatula to cut squares from the pan to serve.
To store, cover the baking pan with aluminum foil and put in the refrigerator for up to 5 days. To reheat, place the entire baking pan in the oven heated to 350 degrees and bake it for about 15 to 20 minutes.