Place butter and minced shallot in a 1-quart sauce pot over medium heat. Cook until translucent. Add morels and a pinch of salt. Cook for 3 minutes, stirring occasionally. Add white wine and reduce by two-thirds. Add heavy cream, turn down the heat and simmer for 20 minutes, until the sauce coats the back of a spoon.
Season with salt and pepper to taste. Keep warm until ready to serve with chicken breasts.