In a medium sized sauté pan, whisk together the basil pesto and heavy cream over medium/low heat.
Add the mushrooms and diced tomatoes and mix until covered with the pesto sauce. Let simmer down for about 5-10 minutes. Do not let the pesto burn, turn the heat down a bit if necessary.
Sprinkle the salt, pepper, and rosemary over the raw chicken breasts and nestle in the pesto mixture to cook. Cover and let cook for 20-30 minutes. Depending on the thickness of breast, can take up to 30 minutes. Insert a meat thermometer to tell when chicken is done cooking (when chicken reaches 165 degrees Fahrenheit).