In a large bowl, beat butter and sugars together with an electric mixer until creamy. Add egg white and vanilla and mix until well blended.
In a medium bowl, combine flour, baking soda, salt and cocoa powder. Gradually add flour mixture to egg and sugar. Use a wooden spoon to work the dough together. Don’t worry if the dough seems a little crumbly at first. Stir in chocolate chips.
Drop cookie dough by the teaspoonful on to a cookie sheet lined with parchment paper or a silicone mat if you have one.
Bake for 8-10 minutes. Cool on cookie sheet for 1 minute, then transfer to wire rack to cool completely.