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Place the nuts in a non-permeable container. Make sure that the container itself is clean and dry, and that the lid of the container snaps or screws on with an airtight seal.  Note that insect eggs and larvae are not an issue when you plan on refrigerating freshly harvested nuts. Even if there are eggs on the nuts you harvested, prolonged storage in cool temperatures should prevent those eggs from hatching. Glass and plastic jars are better than plastic bags. Nuts have a tendency to absorb odors, so the container must have a good seal and should be made from non-permeable material. Otherwise, the flavor of the nuts could become tainted during storage. Place the container of nuts in a refrigerator set to 40 degrees Fahrenheit (4 degrees Celsius) or below. When stored in this manner, most nuts will last for one year. Some varieties may go rancid quicker than that, however.  Almonds, pecans, pistachios, and walnuts should remain fresh for one year. This is true regardless of whether you keep them in their shells or remove the shells prior to storage. When kept in their shells, chestnuts will only stay fresh for two to three months in a refrigerator. When the shell is removed, chestnuts can remain fresh for one year. Chestnuts are high in starch and lose moisture quickly, so they go rancid faster than most other nuts do. Heat and light can make the nuts go rancid faster, so storing them in a dark, cold place lengthens the amount of time the nuts stay fresh.
Pack the nuts in glass or plastic containers. Chill the nuts for two months to one year.