Cook chicken in a large pot of boiling water. Once fully cooked, carefully take the chicken out of the water using a slotted spoon and shred the chicken with two forks.
In a medium bowl, mix soup, salsa, and broth together. Scoop out 2 cups and set aside.
Mix in shredded chicken with the remaining soup/broth mix.
Put 1 cup of the broth mixture that you set aside in the bottom of a 13x9 inch baking dish.
Scoop 1/3 cup of the chicken into the middle of a tortilla. Put 1/2 of a cheese slice on the chicken. Fold sides of the tortilla over the filling and transfer burrito to the 13x9 inch baking dish. Do this with the rest of the tortillas/chicken.
Pour remaining 1 cup soup mixture over the burritos and top with the remaining 2 cheese slices, broken into smaller pieces.
Bake, uncovered, 8-10 minutes, or until cheese is melted and slightly browned.