Line a 28 x 20-cm (11 x 8-inch) pan with plastic wrap. Set aside.
In a large pot of salted water, cook the potatoes until very tender. Drain well.
With a masher, purée the potatoes. Add the cheese, chicken, and one egg and stir to combine. Season with salt and pepper. Spoon into the pan and press evenly. Cover with plastic wrap and refrigerate for at least 3 hours.
Preheat the oil in the deep fryer to 190 °C (375 °F). Line a baking sheet with paper towels.
Place the flour on a plate, the three remaining eggs, lightly beaten, in a shallow bowl and the breadcrumbs in another plate.
Unmould the chilled mixture on a floured surface and cut into 36 sticks, 6 by 6. Flour the sticks and shake to remove any excess. Dip in the egg mixture and drain. Press in the breadcrumbs to coat.
Fry 6 to 8 sticks at a time in the oil for about 2 minutes or until golden brown. Drain on the baking sheet. Serve immediately with Sundried Tomato Mayonnaise or freeze.
To serve frozen pre-cooked sticks, reheat them for 15 to 20 minutes on a baking sheet in the center of a 180 °C (350 °F) preheated oven.