Prepare the Filling: In a large saucepan, heat 3 tablespoons of olive oil over medium heat. Add the coleslaw mix and sauté until it becomes limp, about 3-4 minutes. Add the shredded chicken and sauté for an additional 2-3 minutes, until well mixed. Season with salt and pepper, then turn off the heat.
Assemble the Egg Rolls: Place an egg roll wrapper in front of you, angled so it looks like a diamond. Spoon ¼–⅓ cup of the slaw and chicken mixture horizontally across the middle of the wrapper. Fold in the left and right sides of the wrapper, then roll up from the bottom to enclose the filling. Dab a little water on the edges of the wrapper to seal it closed.
Fry the Egg Rolls: Fill a medium frying pan with about ¾ inch of vegetable oil and heat over medium-high heat to 350–375°F (175–190°C). Working in batches if necessary, fry the egg rolls in the hot oil until they are golden brown on both sides, about 2-3 minutes per side.
Serve: Serve the egg rolls warm with your favorite dipping sauces, such as soy sauce, sweet chili sauce, or sweet and sour sauce.