Fill a deep fryer or a large heavy bottomed pot with enough oil for the chips to easily float. About 2-3 inches. Using a deep-frying thermometer, preheat the oil to 350°F.
Working in batches as needed, submerge the tortilla pieces in the oil trying to keep them from overlapping. Let them fry for 45-60 seconds or until the bottoms just start to brown on the edges. Use a metal slotted spoon or a kitchen spider to flip them. Fry an additional 45-60 seconds or until done.
Remove the homemade tortilla chips from pot and allow the excess oil to drip off. Transfer to a baking sheet lined with paper towels and immediately season with salt. Add a spritz of fresh lime or lime juice as desired.
This recipe makes about 12 tortilla chips per person.
Homemade tortilla chips stay fresh up to three days when stored at room temperature. Keep them in air tight container for best success.
If you need to keep the chips warm, place a baking sheet in the oven heated to the lowest possible setting. Make sure to NOT have the paper towel on the baking sheet, and try not to keep them in there for more than 15 minutes or they might start to overcook.