In a medium bowl, mix together 3/4 pound ground chicken, 1/4 cup thinly sliced scallions, 2 finely chopped garlic cloves, 1 tablespoon toasted sesame oil, 2 1/2 teaspoons soy sauce and 2 1/4 teaspoons chili-garlic sauce. Lightly beat 1 egg in a bowl. Working with 1 piece at a time, brush the edges of square wonton skins with the egg wash and place 1 teaspoon of the chicken mixture in the center of each; fold over to form triangles and press the edges to seal. In a large skillet, heat 3 tablespoons vegetable oil over medium heat. Working in batches, fry the potstickers until golden, adding oil as necessary, about 1 minute per side. Serve warm.