In a large bowl, use an electric mixer to cream together shortening, butter, brown sugar and granulated sugar. Add the eggs, one at a time, mixing until well combined. Mix in the vanilla extract.
In a separate bowl, sift together flour, baking soda and salt. Add the dry ingredients to the butter mixture; mix to combine. Stir in the chocolate chips. Cover and chill for at least 2 hours.
Preheat oven to 375° F. Line baking sheets with parchment paper or silicone mats.
Drop dough by rounded tablespoons two-inches apart on the prepared baking sheets.
Bake for 9-10 minutes, or just until light brown around the edges. The centers will still be soft.
Cool on the baking sheets for about 3-5 minutes, then transfer to wire racks to cool completely.