Preheat the oven to 350°F. Line two to three baking sheets with parch- ment paper or silicone baking mats.
In a large mixing bowl, cream together the butter and sugars with an electric mixer. Scrape down the sides and add the egg and rum (or vanilla extract). Blend well until incorporated.
Add the flour, baking soda, salt, and chips. Mix with the electric mixer until well blended. The dough will not be one big blob. You will need to make the dough stick together with your hands.
Form the mixture into walnut-sized balls and place about 2-inches apart on the prepared trays. Bake for 12 minutes or until golden brown and crackled. Cool on a rack. Cookies will firm up as they cool.
Notes
To freeze: store cooled cookies in an airtight container in the freezer for two to three months -- if they last that long!