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While vegetable, safflower, corn, or peanut oil are all perfectly viable options, many people are increasingly turning to olive oil because it contains no trans fats. Since deep-frying is already the least healthy method of cooking potato chips, it might be a good idea to use the healthiest oil you can get. Optimally, use about a quart of oil. At the bare minimum, cover the bottom of your pan with an inch of oil.  Use a candy thermometer to check the temperature of your oil. If you need to eyeball things because you don't own a candy thermometer, stick the end of a wooden spoon into the oil and wait for bubbles to start forming at the end of the spoon.  Another way to check the temperature of oil without a thermometer is by frying a small cube of bread. Bread will turn a golden hue at 320° F after 30 seconds; 355° F after 15 seconds; and 375° F after 10 seconds.
Choose an oil you'd like to fry with. Heat your oil in a deep fryer or a large frying pan until it reaches about 350° to 375° F (177° to 190° C). Finished.