Hi, I tried searching this up but couldn't find any discussion or addressing of this.
phpBB, which CS is based on, is GPL code. Meaning that if you make changes to it, and share that modified software, you are also required to share the source code. I'm not sure if this is exempted by CS being hosted software (i.e. you're not technically distributing the CS server software, which is what would be affected by GPL—I'm connecting to the CS server from my own web browser as a client), but in any case, I think it would be in the spirit of phpBB's licence and of the philosophy behind phpBB making their software free and open source, to also open source Chicken Smoothie.
If there has been previous discussion of this, do feel free to link me to it. And if I've missed CS's source code being already public, then also feel free to link me to that.