Preheat the oven to 350 degrees F (175 degrees C). Grease 2 baking sheets.
Beat together margarine, peanut butter, sugars, egg, and vanilla in a large bowl with an electric mixer until light and fluffy. Add flour, baking soda, and salt; mix until well combined. Chill dough in the refrigerator for 15 minutes.
Roll chilled dough into walnut-size balls and place 2 inches apart onto the prepared baking sheets.
Bake in the preheated oven until edges are lightly browned, 7 to 10 minutes. Do not overbake. Cool cookies on a wire rack, then store in an airtight plastic container to keep soft.
