I only found one actual Chrome extensions that actually works that does something like what you want, FVD Video Downloader, which can download video and audio. However don't think it is aimed specifically at streaming audio. There is one on the store but all user reviews indicated it does not work. The more conventional way is to install a audio recorder like Audacity or Free Sound Recorder and then select the right audio output (like wave out or something similar) to record and then either manually record your audio or put it on a timer or similar. Some recorders allow you to stop the recording during silence and then continue with a new track.
See the links below for more information. FVD Video Downloader Free Sound Recorder.
It’s able to record your webcam, desktop or specific Chrome tabs, and excellent audio support means you can capture microphone, tab or system audio.
There are millions of users are using Google Chrome browser for surfing net. And Google Blogger platform user must use chrome browsers.
If you are an advance user of Google Chrome then you will notice that Google chrome is included chrome web store. You will find many apps and extensions that will enrich your browsing experience.
Interestingly there are many extensions available on Google Chrome store for screen capturing. And all extensions are very light weight and it will take less than 1 minute to install extension on your Google Chrome browser. How to get Extension from Google Chrome Web Store? This is most amazing screen capturing chrome extension in Chrome Web Store. FireShot ranked best of the year in 2013 from PC MAG. This is very easy to use this screenshot capture tool. By using FireShot you can capture either full webpage, Visible part of a webpage or able to capture selected portion of any webpage.
In addition you can edit captured image for crop, resize, add text and arrow annotations, Blur areas and apply other effects. Finally you can save your screenshots in JPEG, PNG, BMP and PDF format. In Pro version you can send the captured image to Photoshop, clipboard or email directly. You can understand by its name, this screen capturing extension really awesome.
You can capture any web page screen entirely and part of any web page. In addition it will allow you to add annotations, comments, blur sensitive info and share with one click uploads. Through “Awesome Screenshot” you can capture desktop also, this is not possible by other screenshot capturing tool. Formerly Awesome Screenshot offer premium features for paid users, but now they made this extension completely free. So use all premium features free of cost.