In a large bowl, add 2 tablespoons of the soy sauce and the chicken. Toss to coat and place in the fridge to marinate for about 30 minutes. Once marinated, remove from fridge and set aside.
Bring a large pot of salted water to a boil. Add the egg noodles and cook until almost tender, but still has a bite. Drain and set aside.
In a medium bowl, whisk together the remaining soy sauce, brown sugar, lemon juice and chili garlic sauce. Set aside.
Heat a tablespoon of olive oil in a large non-stick skillet over medium-high heat. Add the chicken and cook for about 5 minutes or until brown on all sides. The chicken doesn't need to be cooked all the way through at this point. Transfer the chicken to a plate.
To the same skillet, add another tablespoon of olive oil. Add the bok choy stalks (the white part) and cook for about 3 minutes. Stir in the bok choy leaves and cook for an additional minute, or until wilted. Transfer the bok choy to the plate with the chicken.
Add the remaining 1 tablespoon of olive oil to the skillet and add the egg noodles, sauce you made earlier, and 1 cup of water. Cook for 2-3 minutes or until the noodles are fully-covered in the sauce. Stir in the chicken and bok choy and cook for 5-6 minutes more or until the chicken is cooked through. Stir in the cilantro and season to taste.
Transfer the drunken noodles to a serving platter and sprinkle with green onion. Serve with lemon wedges and enjoy immediately.