In a large saucepan, heat olive oil over medium heat. Add coleslaw and sauté until limp.
Add shredded chicken and sauté for 2–3 minutes, until well mixed. Season with salt and pepper and turn off the heat.
Place an egg roll wrapper in front of you, angled so it looks like a diamond. Add ¼–⅓ cup slaw and chicken mixture horizontally across the middle of your egg roll wrapper.
Fold in the left and right sides of the wrapper, then roll up from the bottom to enclose the filling. Add a little water to the edges of the wrapper to seal so it sticks.
Fill a medium frying pan with ¾ inch oil and heat over medium-high heat to 350–375°F. Working in batches if necessary, fry egg rolls in the hot oil until golden brown on both sides. Serve warm with your dipping sauce of choice.