Fill a large saucepan one-third full of oil and heat to 180°C (350°F), or until a cube of bread browns in 15 seconds. Deep-fry the tortilla pieces in batches for about 30 seconds until golden and crisp. Remove with a slotted spoon and drain on kitchen paper.
Place the chillies in a heatproof bowl, pour over boiling water and leave to soak for 30 minutes.
Meanwhile, heat a dry nonstick frying pan until hot, add the tomatoes and cook for 10 minutes, turning frequently, until starting to char. Add the garlic and cook for a further 2 minutes until charred all over. Transfer to a food processor or blender.
Drain the chillies, reserving the water. Add to the blender with 2 tablespoons of the soaking water and whizz to a smooth paste. Transfer the paste to a saucepan, add the chicken, season and simmer for 5 minutes.
Place the deep-fried tortilla chips in a heatproof serving dish, then pour the sauce all over the chips. Place in a preheated oven, 160°C (325°F), Gas Mark 3, for 5 minutes, or until heated through. Scatter with the coriander and feta.