In a medium skillet, cook the chicken, garlic and ginger until the insides of the chicken are no longer pink, around 5 minutes.
Mix in 3/4 cup of chicken broth, soy sauce and white sugar. Cover and cook for 5 minutes, stirring occasionally
Add in the broccoli. Cover and cook for an additional 5 minutes.
In a small bowl, mix together the 1/4 of remaining chicken broth with the cornstarch.
Add the snap peas and the cornstarch mixture to the chicken mixture, and mix until the sauce begins to thicken.