To expand a little, I think the biggest issue that Chelsea has with a grand jury is that the entire process is sealed. If it were a public hearing then she would be much more likely to testify, because we would know what was asked, what was answered, and we would know what this entire process is about.

We only assume that this grand jury is about Julian Assange (because what else would Chelsea's testimony be relevant for?), but we actually don't know. This could be a political witch hunt for any variety of reasons, and we might never find out. An opaque justice system is probably not a good thing, since we just have to trust that the people in charge will do the right thing- and we have seen countless times throughout history that the people in charge often do the wrong thing and attempt to cover it up.