Heat a little olive oil in a large, deep skillet. Cook the chicken over medium low to medium heat until mostly white, with just a hint of pink. Transfer chicken to platter and drain oil from pan.
Mix water and Italian dressing mix in a bowl or measuring cup. Return chicken to the pan and pour the salad dressing mix over it. Cover and simmer for 10 minutes.
Mix the cream cheese and cream of chicken soup together. Pour the mixture over the chicken and cover again. As it heats all the way through the dressing mix and water will rise. Stir occasionally until everything is blended and the chicken is cooked, about 15-20 minutes on medium.
About 5 minutes before serving, add the mushrooms and stir, then heat through.