In a medium bowl, whisk flour, baking soda, and salt. In the large bowl of a stand mixer fitted with the paddle attachment, beat brown sugar, butter, and granulated sugar on medium-high speed until pale and fluffy, 2 to 3 minutes.
Beat in egg and vanilla until combined, then reduce speed to low and beat in dry ingredients until incorporated. Fold in chocolate chips and 2 cups potato chips. Cover bowl and refrigerate 1 hour.
Arrange racks in upper and lower thirds of oven; preheat to 350°. Line 2 baking sheets with parchment. Place remaining 3/4 cup potato chips in a small flat dish.
Scoop dough into balls about 3 tablespoons (2 ounces) each. Roll in potato chips, gently pressing to adhere. Arrange on prepared sheets, spacing about 1" apart. With a clean palm, flatten balls into pucks about 2 1/2" in diameter.
Bake cookies, rotating sheets top to bottom and back to front after 7 minutes, until puffed and golden brown around the edges, 11 to 14 minutes.
Let sit 2 minutes on baking sheets, then transfer to a wire rack and let cool completely.
Make Ahead: Cookies can be made 3 days ahead. Store in an airtight container at room temperature.