Unfortunately, not all Zotero features are available on a Chromebook.
You can also try using one of the campus virtual Windows options. You basically remotely login to a HSU campus computer and can do anything that can be done on that computer. See below for more details about remote access at HSU.
You can access most of the software available on campus computers from off-campus using Remote Access or the Virtual Lab (VLab). This includes MS Office, Adobe Creative Cloud, Camtasia, and many more programs that would otherwise be expensive to purchase. If you are having issues accessing these services, visit the ITS System Status page to make sure they are working properly.
Remote Access (Chromebooks, Macs, and Windows) allows you to login to an HSU computer over the internet. You will have access to all of the software on that computer. You will need to install a program to make the connection (the remote access page includes instructions).
VLab (all computers with internet access) allows you to login to a virtual desktop that includes software typically available in HSU computer labs (current list of VLab software). Does not require any connection software.