Exposure to air causes cheese to dry out. If your apartment is not equipped with a pantry or cellar, the best place to store chèvre is in the vegetable drawer of your refrigerator. Keep pieces wrapped in plastic wrap or wax paper, or place in a sealable bag and squeeze out the air. Fresh cheese can be enjoyed straight out of the refrigerator. Soft-ripened and aged cheeses should come to room temperature for an hour for optimal flavor.