Papyrus

Dropbox's Paper is a newly-launched collaboration service that aims to make creating, sharing and maintaining documents as effortless as possible. Basically, it provides a unified environment where you and your team can chat and work in real time on various projects.
Since Paper is still in Beta, Dropbox has yet to announce an official desktop client, so it may seem that you are forced to make use of your web browser, unless, you give Papyrus a quick spin.

Unofficial and uber-simplistic client for Dropbox Paper

Papyrus is an unofficial, Electron-based wrapper for Dropbox Paper which means that it allows you to work with your team members on projects without having to rely on a web browser.
You can start taking advantage of what this wrapper proposes in practically no time, since it does not even require installation. Simply download Papyrus, unzip its package and launch it via its designated executable.

The same, simple login procedure

As expected, once you start up the app, you will be prompted to log in using your official Dropbox credentials. This is a good opportunity to point out that working with it depends on your Dropbox account's pricing plan.
Also quite evident is the fact that Papyrus brings the full functionality of Dropbox Paper to your computer's desktop. You will benefit from the same user-friendly interface, the same word-processing, and document-sharing, as well as other, more advanced collaboration tools.

Work with Dropbox Paper directly from your computer's desktop

Of course, we would have liked if the utility would provide some extra features. For example, it would have been quite nice if Papyrus would feature taskbar integration. Nevertheless, in the current situation at least, it's no point on bickering about such matters since it's currently the single (albeit it being unofficial) solution for working with Paper outside your web browser.