Alternatively, it could be refering to gambling. In the casino, you play with those little round discs that we call "chips". A stack of chips would imply that you are gambling with a lot of money - a pile of them = a stack. This can be metaphoric too...you are taking a big risk with/on something.

"to have a chip on your shoulder" = "to be easily offended or argumentative, or emotionally distant, because you have a grudge (against this person or someone from the past)" It is usually not said as "to have a STACK of chips on your shoulder." But this would imply that you are VERY easily offended and VERY QUICK to argue or push people away emotionally, for different reasons.