Prepare oven by preheating to 375 degrees.
Combine sugar and brown sugar in a small bowl. Set aside.
Thoroughly mix flour, baking soda and salt in a mixing bowl. Stir in chocolate chips, oats, and walnuts.
In a separate mixing bowl, cream butter. Add half of sugar mixture. Cream again. Add remaining sugar and cream well.
Add egg and vanilla extract to butter mixture and beat thoroughly.
Blend chocolate oat mixture into butter mixture making sure all ingredients are well mixed.
Drop rounded teaspoonfuls of chocolate oatmeal cookie dough onto an ungreased cookie pan.
Bake approximately 12 minutes or until the cookie edges are lightly browned.
Cool on a wire rack then enjoy!