It seems that LibreOffice is not available for Chromebooks, but you can get Collabora Office from the Google Play Store.
As I understand it, Collabora Office is a version of LibreOffice intended to support collaborative work. It was originally developed by Collabora Ltd. in close cooperation with The Document Foundation, which maintains LibreOffice. Unfortunately, those two organisations seem to have fallen out and are no longer talking to each other.
I think the presumption is that Chromebook users would use the word processing, spreadsheet etc on Google drive - which can also read and display Microsoft office and other formats.
@keithjeremiah Yes, that was my thought, too. But you shouldn't need Google Drive and an Internet connection just to use files on your local machine. And you don't want to be tied in to Google products any more than you have to. Microsoft and Apple users won't want documents in Google formats and having to export your Google files to something more portable is a nuisance.