Preheat oven to 350 degrees F. Grease a 9 x 13-inch baking dish and set aside.
In a large bowl, use an electric mixer to cream together butter, white sugar and brown sugar for 3 minutes. Scrape the bowl, then add the eggs and vanilla. Beat for another 3 minutes, scraping the sides as necessary.
Slowly add flour, baking soda and salt. Beat for 2 minutes.
Fold 1 ½ cups of the chocolate chips, just until combined.
Spread the dough evenly in the greased baking dish. Top with the remaining ½ cup of chocolate chips, pressing down gently into the dough.
Bake for 25-30 minutes, or until the top is lightly brown and the bars are slightly firm to the touch. For chewy bars, do not overbake (maybe even under-bake slightly!).
Transfer the pan to a wire rack to cool completely. Once cool, slice into squares and serve!