In the bowl of a standing electric mixer fitted with the paddle, beat the butter, brown sugar, granulated sugar, eggs and vanilla at medium speed until light and fluffy, about 5 minutes. In a medium bowl, whisk the flour with the baking soda and salt. Add the dry ingredients to the mixer and beat at low speed until incorporated, scraping down the bowl occasionally. Stir in the chocolate chips. Cover and refrigerate the dough until chilled, about 1 hour.
Preheat the oven to 350° and line 2 large baking sheets with parchment paper. Scoop up 2 tablespoon–size clumps of the dough and roll into balls. Place the balls on the baking sheets about 3 inches apart (the cookies will spread quite a bit). Bake in the lower and middle thirds of the oven for about 17 minutes, until the cookies are lightly browned around the edges but still very soft in the center; shift the pans from top to bottom and front to back halfway through baking. Slide the parchment onto racks and let the cookies cool. (Run the baking sheets under cold water between batches.) Repeat with the remaining dough. Serve the cookies warm or at room temperature.