Preheat oven to 350 degrees F (175 degrees C). Grease cookie sheets.
In a medium bowl, cream together the butter, brown sugar, and white sugar until smooth.
Beat in the egg and vanilla.
Combine the flour, baking soda, cinnamon and salt; stir into the creamed mixture.
Mix in the oats.
Drop by rounded spoonfuls onto the prepared cookie sheets.
Bake for 10 to 12 minutes in preheated oven. Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.