Cook noodles according to package directions until tender. Drain and rinse in cold water. Set aside.
Heat oil in a large skillet over medium heat. Brown the chicken on both sides, about 5 minutes.Remove to a plate.
Add the garlic, bok choy and mushroom caps (halve or quarter, if necessary) to the skillet and raise the heat to high. Cook vegetables, stirring often, until they are tender, about 5 minutes.
Add broth and stir, scrapping up the brown bits. Add the soy sauce, sesame oil and the chili oil. Add the chicken, reduce to low, and simmer until the chicken is cooked through, 3 to 5 minutes. Remove from heat.
Stir in the noodles and top with the green onions.