Preheat oven to 350°.
In a large bowl, beat butter, sugars and peanut butter until creamed. Add egg, vanilla and beat until fluffy.
In another bowl, combine flour, salt and baking soda. Add to creamed mixture and mix well. Stir in rolled oats.
Roll dough into 1 inch balls and place about 2 inches apart on ungreased baking sheets. Slightly flatten each cookie with the bottom of a glass dipped in sugar.
Bake for 10 - 12 minutes or until lightly browned.
Makes about 4 dozen.