Preheat the oven to 180°C. Lightly grease 2 baking sheets.
Cream the butter and sugars together until light and fluffy. Beat in the egg and vanilla. Sift in the flour and baking soda and beat into the mixture. Add the chocolate chips and nuts and stir until well combined.
Drop large, rounded tbsp of the dough on to the baking sheets, 5 or 6 per sheet, well-spaced as the cookies will spread.