Anime Wings
The Anime Wings are a pair of wings Chris got at Anime Mid-Atlantic convention that are clipped on to the hair. This accessory is usually used by women, specifically, otaku fangirls (well really, how often do men wear hairclips). Chris's pair somehow turn real when he transforms into Super Chris-Chan Sonichu if he transforms while wearing them. This gives Chris-chan even more god-like abilities, granting him the power to fly.
The wings first appeared in Sub-Episode 4 and are promptly knocked off of his head at the beginning of Sub-Episode 5, where they are... destroyed? Lost forever? Forgotten? Either way, Chris-Chan Sonichu has been shown to be perfectly capable of flying without them (probably because it's easier to draw).
Super Chris-Chan Sonichu
With the Anchuent Powers, Chris-Chan can transform into Super Chris-Chan Sonichu if he has his anime wings on top of his head. They appear to be similar looking to Angelica's. Considering him doing this would make him super, thus more powerful than his original form, he would be wise in using this to his advantage in future comics. But alas, this concept was completely forgotten about by Chris, just like the plot in Sonichu. Honestly, what happened to Metal Sonichu, or Bill The Scientist?
Another note to be made is that Chris-Chan cannot come up with an original idea, so this had to be ripped off from somewhere. Due to his influence with Nintendo, he most likely got the "Super" part of the name from Super Nintendo and the fact that many titles in the SNES collection consisted of "Super" in their name. As for the actual wings part, it is probably stolen from Super Mario Bros.'s Koopa Paratroopas, or from some anime. Super Mario 64 has the wing cap that allows Mario to fly, so the former is more likely.