Chikane did shoot Soma, but she needed him alive to get Himeko to the Moon. Himeko had exactly one other friend who barely had any narrative presence. And really, Himeko would have performed mental gymnastics anyways-- "Chikane doesn't hate me, she only hates my friends out of jealousy, so if I show my love for her she'll stop being evil." The point of raping Himeko is to make her believe that Chikane's love is perverse and non-genuine, that Chikane sees Himeko as merely an object of attraction rather than a partner. If Himeko believes there is even a shred of genuine affection on Chikane's part, she would rather take the blame and die than hurt Chikane. To corrupt her own image in Himeko's mind, she has to attack Himeko directly, and rape is the most emotionally charged way of doing so. There's torture, but that really isn't any better-- it's just as "psycho" but less "lesbian."
And on that note, Chikane isn't psycho-- she has her issues, yes, namely her guilt complex for killing Himeko and gayngst. But her actions were calculated, her end goal was noble, and her methods were logical under her circumstances.