Preheat peanut oil in deep-fryer to 375 degrees F.
Peel potatoes and then slice into very thin 1/8-inch slices using a mandoline with a straight blade attachment. Keep potatoes in very cold water until ready to fry after cutting. Drain potatoes in a colander and blot dry with paper towels.
Fry potatoes in batches, only a few at a time, for about 3 to 4 minutes. Once they reach a golden brown color, remove chips from the fryer and drain on a pepper towel lined sheet tray. Dust immediately with salt, pepper and Neely's BBQ seasoning, to taste.