Is there any game development software (specifically, one that’s free of charge and doesn’t contain viruses or malware) for Chromebook?
Do you mean developing on a Chromebook, or developing for Chromebook (ie. HTML5, Android)?
There are these for working on a Chromebook:
For developing HTML5 or Android (more or less Java) there are lots of free tools: NetBeans, Eclipse etc.
Strictly speaking, at least for web tech, all you need is a text editor.