Preheat the oven to 375 degrees F. Whisk the flour, baking soda, baking powder and salt in a medium bowl. In a large bowl, beat the butter, granulated sugar and brown sugar with a mixer on medium-high speed until pale and fluffy, 3 minutes. Beat in the eggs, one at a time, then the vanilla. Reduce the mixer speed to low; beat in half of the flour mixture until just combined. Beat in the sour cream, then the remaining flour mixture. Stir in the chocolate chips. Chill, 30 minutes to 1 hour.
Drop heaping tablespoonfuls of dough 2 inches apart onto parchment-lined baking sheets. Bake, one baking sheet at a time, until the cookies are puffed and the edges are set, 8 to 12 minutes. Let cool 5 minutes on the pans, then transfer to a rack.