Preheat oil in a large saute pan to 340 degrees (don't let it rise above 350 or chips will cook too quickly and burn). Line a 13 by 9-inch baking sheet with 2 layers of paper towels.
Make four stacks of 5 tortillas each and cut through each stack into 6 wedges (like cutting a pizza).
Working quickly add 15 wedges (or just enough to fit) to preheated oil in a single layer. Let cook until chips curl slightly, about 20 seconds then using a spider strainer collect as many chips as possible at once and flip to opposite side, repeat with any chips remaining until all have been flipped.
Let cook on opposite side about 20 seconds, or just until they turn just barely a shade darker (not browned!). Collect as many chips as possible in spider strainer, carefully shake excess oil from chips back into pan and transfer to paper towels to drain. Repeat, quickly collecting any remaining chips, season with salt.
Repeat frying and draining process. Scoot cooled chips on paper towels to one side to make room for more chips to drain.
To Make Baked Tortilla Chips
Preheat oven to 350 degrees. Grease two 18 by 13-inch baking sheets.
Brush both sides of 12 extra thin corn tortillas with 1 1/2 Tbsp oil (total). Stack and cut into 6 wedges.
Align in a single layer on prepared baking sheets. Bake in preheated oven on two oven racks near center, 7 minutes.
Rotate pans then continue to bake about 7 minutes longer, or just until chips edges turn lightly golden brown. Season with salt and let cool.
Standard corn tortillas can be used here as well just increase baking time by a few minutes.