Google Reader Notifier (by Google) is an official Chrome extension by Google, which provides you with an unread count and notifications for your Google Reader feeds. You can preview, mark (as read) and manage the feeds from your Google Reader account within a minimalist interface.
Such extensions are quite common for online account management and add a lot of convenience for users who wish to check their online accounts from time to time without having to visit the website of the respective web service. An example can be the Dropbox extension which provides similar functionality for Dropbox users.
Once Google Reader Notifier is installed, it instantly displays an unread mail count for your Google Reader feeds (provided you are logged into your Google Account).
You can click on the Google Reader icon to open a pop-up window for managing you Google reader feeds. For example, you can use the drop down menu to select a feed category to view your feeds and mark unread feeds as “read”. The Refresh option refreshes the feed list, whereas, Open Google Reader option opens Google Reader in a new window. You can click on the up/down arrows to move vertically across a feed list.
Google reader Notifer might not have a complete range of management options for Google Reader account management, however, it does provide some minor options which are enough to keep an eye on new and unread RSS feeds.
Install: Google Reader Notifier Extension for Chrome