Preheat the oven to 220C/425F/Gas 7.
Place the vegetable oil into a deep, heavy-bottomed saucepan and heat until a small cube of bread sizzles and turns golden when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Carefully place the chips into the hot oil and cook for 6-7 minutes. Remove the chips from the oil using a slotted spoon and drain on kitchen paper.
Place the chips onto a baking sheet and transfer to the oven to roast for 8-10 minutes, or until golden and crisp. Remove the chips from the oven, sprinkle with salt and set aside to keep warm.
For the pesto, place all of the ingredients into a small food processor and blend until smooth.
To serve, place the chips into a bowl and pour over the pesto.