It is possible to get this before you arrive at the Sierra Madre.
In the Brotherhood of Steel bunker that you trace the initial signal in the Mojave to contains a Sierra Madre Vending machine with with you can exchange cartons of cigarettes for Sierra Madre chips at a rate of 20 chips per carton so simply collect 25 cartons and exchange them at the Brotherhood of Steel bunker.
There are 19 cartons located throughout the lucky 38 casino, 7 at Mojave outpost, 5 at Mick and Ralph's, 5 at Jacobstown Lodge and 4 scattered through Helios One.