Is a partially frozen chicken safe if not immediately cooked at the proper temperature?
Assuming you thawed the chicken (to the extent that you did) in the refrigerator, and further assuming that it took less than an hour to reach a safe internal temperature, I would say you are fine. An internal temperature of 180ºF (80ºC) is safe by quite a margin.

The USDA recommends that home cooks do not keep food within the "Danger Zone" of 40-140ºF (4-60ºC) for more than 2 hours. This includes preparation and cooking time. If you thawed the bird on the kitchen counter, or if your chicken accompanied you on a long journey from the supermarket in an unfrozen state, you'll have to factor that time in.

As @Jefromi's comment on another answer notes, simply reaching a high enough internal temperature is not a guarantee of safety since some microbes produce toxins that are heat-stable.