Chop the chicken into small pieces. Slice the 2 grilled scallions and combine them with the chopped chicken. Slice the uncooked scallion and set aside for garnish.
Put the wrappers onto a clean work surface and put 1 teaspoon of the chicken into the center. Dip a finger into some water and moisten the edges of the wonton. Fold the wrapper over and pinch the edges together, making 3 or 4 pleats. Repeat with remaining ingredients.
Heat a large nonstick skillet with canola oil over medium heat. When the oil is hot, add the wontons in 1 layer. Let cook until the bottoms are browned, about 2 to 3 minutes, then add 2 tablespoons water. Quickly cover and cook until the wrappers are tender, about 3 minutes.
Whisk together the soy sauce, vinegar, sugar, and 2 tablespoons water in a small bowl. Stir until the sugar has dissolved and set aside.
Arrange the pot stickers on a serving platter, garnish with the reserved sliced scallions and serve with the dipping sauce.