In a large saucepan, heat the olive oil over medium heat. Add the coleslaw mix and sauté until it becomes limp.
Next, add the shredded chicken to the saucepan. Sauté the mixture for 2–3 minutes, stirring until everything is well combined. Season with salt and pepper as desired, then turn off the heat.
Now, take an egg roll wrapper and place it in front of yourself, angled like a diamond. Pour about 1/4 to 1/3 cup of the coleslaw and chicken mixture horizontally across the middle of the wrapper.
Fold the left and right sides of the wrapper in toward the center, then roll it up from the bottom, enclosing the filling. Use a little water to moisten the edges of the wrapper, sealing it tightly.
In a medium frying pan, fill it with about 3/4 inch of vegetable oil. Heat the oil over medium-high heat until it reaches 350–375°F.
In batches if necessary, carefully fry the egg rolls in the hot oil until they turn golden brown on both sides.
Once fried, remove them from the oil and place them on a paper towel-lined plate to drain any excess oil.
Serve the egg rolls warm, accompanied by your favorite dipping sauce.