Three cup chicken is so-called because the traditional recipe uses one cup each of rice wine, soy sauce and lard. In today’s day and age that amount of lard is totally unacceptable, and so this has been changed and modified to be more acceptable to modern tastes by replacing the lard with chicken stock.
However, it is still a chicken-only recipe. I have modified this further as I think this just enhances the dish and makes it more of a complete one-pot meal, removing the need for an additional side-dish. You could make it with chicken only, but then I would recommend some steamed veg (e.g. pak-choi with ginger and soy) as an accompaniment.
This recipe uses shiitake mushrooms and Pak choi, but you could substitute either of these with other types of mushrooms, green beans, mangetout, etc. Also, due to the addition of soy sauce, there is a fair bit of saltiness already, so be very careful while adding any extra salt.