In a large bowl beat the butter or margarine, granulated sugar and brown sugar together. Add the eggs and vanilla, beating well.
In a medium-size bowl, stir together the flour, baking soda, cinnamon and salt. Gradually add flour mixture to butter mixture; stir until blended. Stir in oats and butterscotch chips. Drop by tablespoonfuls about 2 inches apart onto ungreased cookie sheets.
Bake for 10 minutes, until the edges begin to brown. Transfer to a wire rack to cool.