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In a large bowl, cream together the butter and sugar until light and fluffy.
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Beat in the egg, then stir in the vanilla.
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Combine the flour and salt; stir into the sugar mixture.
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Cover dough, and chill for at least one hour. Chill cookie sheets as well.
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Preheat oven to 400 degrees F.
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Scoop dough out onto chilled cookie sheets.
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Bake for 13 to 15 minutes in the preheated oven, or until lightly golden at the edges.
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Remove from cookie sheets to cool on wire racks.