It's possible to do this achievement almost as soon as the DLC is loaded, before you've gone to the Sierra Madre. Once the DLC is loaded, you can access the "Abandoned BoS Bunker" near Nelson/Forlorn Hope. Go there, and save your game, with a hard save.
When you enter the bunker, continue down the stairs, as if you were going to start to DLC. Open the door that gives you a warning message, but DO NOT WALK ALL THE WAY TO THE NEXT ROOM. Doing so will force you into the Sierra Madre, and you may not be ready yet. Instead, hang your first left, and hack the computer there.
This will open a little room formerly occupied by a BoS knight. In the corner, there is a vending machine. It will dispense food for Sierra Madre chips. It will also give you chips, for cartons/packs of cigarettes.
Cartons and packs of cigarettes are relatively low-weight/high-value items that a lot of people pick up, to sell to merchants. So you might already have a few, or might have recently sold a few to a merchant. Go buy them back. Alternatively, if you've been let into The Strip, and the Lucky 38, the 38's casino floor has a ton of free cartons of cigarettes. there should be enough there to easily net 500 chips.
I made 845, in one shot, from a few I had sold to a merchant, and the ones in the lucky 38.