In a large bowl, combine chicken, mushrooms, garlic, green onions, soy sauce, sesame oil, ginger, rice vinegar and white pepper.
To assemble the potstickers, place wrappers on a work surface. Spoon 1 tablespoon of the chicken mixture into the center of each wrapper. Using your finger, rub the edges of the wrappers with water. Fold the dough over the filling to create a half-moon shape, pinching the edges to seal.
Heat olive oil in a large skillet over medium heat. Add potstickers in a single layer and cook until golden and crisp, about 2-3 minutes per side.