Cook and shred the chicken breast by your preferred method (pan frying, grilling, poaching, baking, etc.) until internal temperature has reached 165F. Allow to cool slightly and shred with two forks.
Mix the shredded chicken with the softened cream cheese, pepper jack cheese, jalapeño half the green onions, garlic powder, and Worcestershire sauce until well combined.
Lay out 4 - 5 wonton wrappers on a large surface. Place 1 teaspoon of the cream cheese filling to the middle of each wrapper. Wet the edges of each wrapper with your finger dipped in water, repeating if necessary in water, and then fold the wonton wrapper in half into a triangle shape. Make sure to press and seal all the edges. Set aside and repeat until you've assembled all the wonton wrappers into Rangoon's.
Fill a bottom heavy, large pot with 3 - 4 inches of vegetable or peanut oil. Preheat until the oil is measuring at 350F. Drop 5 - 6 of the sealed wontons into the hot oil (depending on the size of your pot) and fry for roughly 3 minutes, or until browned and crispy. Drain on paper towels while you work on the remaining wontons.
Serve immediately, garnished with remaining green onions and served with your favorite sauce. I prefer the sweet chili sauce.