Preheat oven to 375 degrees Fahrenheit and go ahead and lay out several cookie sheets.
In a large bowl, use a hand mixer to mix the butter, both of the sugars, pudding mix, eggs and vanilla until creamy.
Add the baking soda to the mixture and then gradually add the flour, while continuing to beat on low speed until all ingredients are well mixed.
Using a spoon, stir in the chocolate chips.
Drop the batter, by tablespoons, onto the ungreased cookie sheets about 2 inches apart. (these cookies didn't spread too much)
Bake for 8-10 minutes, or just until the edges start to brown. (they will look like they are not done, but they are. Be careful not to overcook.
Remove from the oven and let cookies cool.