Now it is possible to use Zotero directly from Chrome, no more opening Firefox just to browse and save papers.
It is recommended to also install Zotero Standalone, as that will work as a central repository for all you Zotero plugins (Chrome, Firefox and Safari). You can make it work with Zotero for Firefox being the central, but it isn't recommended.
Also, you should create a Zotero account to sync up your data to the Zotero server and keep it in a safe place. Definitely the best extension for managing papers