Cream the butter and sugar in a large bowl with a wooden spoon until smooth, about 2 minutes. Stir in the vanilla, then add the flour and salt, mixing until a crumbly dough forms. Fold in the chocolate chips.

Turn the dough onto plastic wrap and shape into a log 2 inches wide and 8 inches long. Wrap tightly and chill for at least 1 hour until very firm.

Preheat oven to 325°F (160°C) and line two baking sheets with parchment. Slice the log into ¼-inch-thick rounds with a serrated knife. Place 1 inch apart on sheets. Bake one sheet at a time on the middle rack for 12 to 14 minutes, until edges are pale golden. Cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.