Preheat the oven to 350 degrees F. With an electric mixer, cream the butter, sugar, and the vanilla, by beating on high for 3-5 minutes until light and fluffy. Then turn the mixer on low and mix in the potato chips and the flour, until well-combined.
Wrap the dough in plastic and refrigerate for at least 30 minutes.
Flour a work surface and roll the dough out to 1/8- to 1/4-inch thick. Using a pizza cutter cut the dough into 1 x 2 1/2 inch strips. Use a small thin spatula to transfer the strips onto parchment paper lined cookie sheets.
Bake the cookies until they are light golden brown, 14-16 minutes.
Remove the parchment paper with the cookies from the sheet and cool on the counter. When cookies have cooled, melt the chocolate with 1 tablespoon butter in the microwave for 30 seconds. Stir and repeat until smooth. Drizzle it over the cookies. Let the chocolate harden before serving.
NOTES: On occasion chocolate will seize (harden up) when you try to melt it. This happens because dealing with chocolate requires tempering (raising and lowering the temperature of the chocolate) with accuracy. However, we are not worried about perfection here--we're just drizzling cookies! If your chocolate seizes, add a little more butter or even some milk. This will cause the chocolate to loosen so you can drizzle it. Later it will firm up again--not quite as hard as pure chocolate--but it will still look and taste great!